Download or read book Kazhdan Lusztig Theory and Related Topics written by Vinay Deodhar and published by American Mathematical Soc.. This book was released on 1992 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume attests to the far-reaching influence of Kazhdan-Lusztig theory on several areas of mathematics by presenting a diverse set of research articles centered on this theme. Although there has been a great deal of work in Kazhdan-Lusztig theory, this book is perhaps the first to discuss all aspects of the theory and gives readers a flavor of the range of topics involved. The articles present recent work in Kazhdan-Lusztig theory, including representations of Kac-Moody Lie algebras, geometry of Schubert varieties, intersection cohomology of stratified spaces, and some new topics such as quantum groups.
Download or read book Kazhdan Lusztig Theory and Related Topics written by Vinay Deodhar and published by American Mathematical Soc.. This book was released on 1992 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume attests to the far-reaching influence of Kazhdan-Lusztig theory on several areas of mathematics by presenting a diverse set of research articles centered on this theme. Although there has been a great deal of work in Kazhdan-Lusztig theory, this book is perhaps the first to discuss all aspects of the theory and gives readers a flavor of the range of topics involved. The articles present recent work in Kazhdan-Lusztig theory, including representations of Kac-Moody Lie algebras, geometry of Schubert varieties, intersection cohomology of stratified spaces, and some new topics such as quantum groups.
Download or read book Kazhdan Lusztig Theory and Related Topics written by and published by . This book was released on 1992 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Representations of Finite Dimensional Algebras and Related Topics in Lie Theory and Geometry written by Vlastimil Dlab and published by American Mathematical Soc.. This book was released on with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings are from the Tenth International Conference on Representations of Algebras and Related Topics (ICRA X) held at The Fields Institute. In addition to the traditional ''instructional'' workshop preceding the conference, there were also workshops on ''Commutative Algebra, Algebraic Geometry and Representation Theory'', ''Finite Dimensional Algebras, Algebraic Groups and Lie Theory'', and ''Quantum Groups and Hall Algebras''. These workshops reflect the latest developments and the increasing interest in areas that are closely related to the representation theory of finite dimensional associative algebras. Although these workshops were organized separately, their topics are strongly interrelated. The workshop on Commutative Algebra, Algebraic Geometry and Representation Theory surveyed various recently established connections, such as those pertaining to the classification of vector bundles or Cohen-Macaulay modules over Noetherian rings, coherent sheaves on curves, or ideals in Weyl algebras. In addition, methods from algebraic geometry or commutative algebra relating to quiver representations and varieties of modules were presented. The workshop on Finite Dimensional Algebras, Algebraic Groups and Lie Theory surveyed developments in finite dimensional algebras and infinite dimensional Lie theory, especially as the two areas interact and may have future interactions. The workshop on Quantum Groups and Hall Algebras dealt with the different approaches of using the representation theory of quivers (and species) in order to construct quantum groups, working either over finite fields or over the complex numbers. In particular, these proceedings contain a quite detailed outline of the use of perverse sheaves in order to obtain canonical bases. The book is recommended for graduate students and researchers in algebra and geometry.
Download or read book Abelian Group Theory and Related Topics written by Rüdiger Göbel and published by American Mathematical Soc.. This book was released on 1994 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of a conference on abelian groups held in August 1993 at Oberwolfach. The conference brought together forty-seven participants from all over the world and from a range of mathematical areas. Experts from model theory, set theory, noncommutative groups, module theory, and computer science discussed problems in their fields that relate to abelian group theory. This book provides a window on the frontier of this active area of research.
Download or read book Finite Dimensional Algebras and Related Topics written by V. Dlab and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on invited lectures at the 1992 Canadian Algebra Seminar, this volume represents an up-to-date and unique report on finite-dimensional algebras as a subject with many serious interactions with other mathematical disciplines, including algebraic groups and Lie theory, automorphic forms, sheaf theory, finite groups, and homological algebra. It will interest mathematicians and graduate students in these and related subjects as an introduction to research in an area of increasing relevance and importance.
Download or read book Lie Algebras and Related Topics written by Georgia Benkart and published by American Mathematical Soc.. This book was released on 1990 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discusses the problem of determining the finite-dimensional simple Lie algebras over an algebraically closed field of characteristic $p>7$. This book includes topics such as Lie algebras of prime characteristic, algebraic groups, combinatorics and representation theory, and Kac-Moody and Virasoro algebras.
Download or read book Representations of Semisimple Lie Algebras in the BGG Category O written by James E. Humphreys and published by American Mathematical Soc.. This book was released on 2021-07-14 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first textbook treatment of work leading to the landmark 1979 Kazhdan–Lusztig Conjecture on characters of simple highest weight modules for a semisimple Lie algebra g g over C C. The setting is the module category O O introduced by Bernstein–Gelfand–Gelfand, which includes all highest weight modules for g g such as Verma modules and finite dimensional simple modules. Analogues of this category have become influential in many areas of representation theory. Part I can be used as a text for independent study or for a mid-level one semester graduate course; it includes exercises and examples. The main prerequisite is familiarity with the structure theory of g g. Basic techniques in category O O such as BGG Reciprocity and Jantzen's translation functors are developed, culminating in an overview of the proof of the Kazhdan–Lusztig Conjecture (due to Beilinson–Bernstein and Brylinski–Kashiwara). The full proof however is beyond the scope of this book, requiring deep geometric methods: D D-modules and perverse sheaves on the flag variety. Part II introduces closely related topics important in current research: parabolic category O O, projective functors, tilting modules, twisting and completion functors, and Koszul duality theorem of Beilinson–Ginzburg–Soergel.
Download or read book Finite Dimensional Algebras and Quantum Groups written by Bangming Deng and published by American Mathematical Soc.. This book was released on 2008 with total page 790 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The interplay between finite dimensional algebras and Lie theory dates back many years. In more recent times, these interrelations have become even more strikingly apparent. This text combines, for the first time in book form, the theories of finite dimensional algebras and quantum groups. More precisely, it investigates the Ringel-Hall algebra realization for the positive part of a quantum enveloping algebra associated with a symmetrizable Cartan matrix and it looks closely at the Beilinson-Lusztig-MacPherson realization for the entire quantum $\mathfrak{gl}_n$. The book begins with the two realizations of generalized Cartan matrices, namely, the graph realization and the root datum realization. From there, it develops the representation theory of quivers with automorphisms and the theory of quantum enveloping algebras associated with Kac-Moody Lie algebras. These two independent theories eventually meet in Part 4, under the umbrella of Ringel-Hall algebras. Cartan matrices can also be used to define an important class of groups--Coxeter groups--and their associated Hecke algebras. Hecke algebras associated with symmetric groups give rise to an interesting class of quasi-hereditary algebras, the quantum Schur algebras. The structure of these finite dimensional algebras is used in Part 5 to build the entire quantum $\mathfrak{gl}_n$ through a completion process of a limit algebra (the Beilinson-Lusztig-MacPherson algebra). The book is suitable for advanced graduate students. Each chapter concludes with a series of exercises, ranging from the routine to sketches of proofs of recent results from the current literature."--Publisher's website.
Download or read book An Introduction to Intersection Homology Theory Second Edition written by Frances Kirwan and published by CRC Press. This book was released on 2006-06-07 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now more that a quarter of a century old, intersection homology theory has proven to be a powerful tool in the study of the topology of singular spaces, with deep links to many other areas of mathematics, including combinatorics, differential equations, group representations, and number theory. Like its predecessor, An Introduction to Intersection Homology Theory, Second Edition introduces the power and beauty of intersection homology, explaining the main ideas and omitting, or merely sketching, the difficult proofs. It treats both the basics of the subject and a wide range of applications, providing lucid overviews of highly technical areas that make the subject accessible and prepare readers for more advanced work in the area. This second edition contains entirely new chapters introducing the theory of Witt spaces, perverse sheaves, and the combinatorial intersection cohomology of fans. Intersection homology is a large and growing subject that touches on many aspects of topology, geometry, and algebra. With its clear explanations of the main ideas, this book builds the confidence needed to tackle more specialist, technical texts and provides a framework within which to place them.
Download or read book Kac Moody Groups their Flag Varieties and Representation Theory written by Shrawan Kumar and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 613 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kac-Moody Lie algebras 9 were introduced in the mid-1960s independently by V. Kac and R. Moody, generalizing the finite-dimensional semisimple Lie alge bras which we refer to as the finite case. The theory has undergone tremendous developments in various directions and connections with diverse areas abound, including mathematical physics, so much so that this theory has become a stan dard tool in mathematics. A detailed treatment of the Lie algebra aspect of the theory can be found in V. Kac's book [Kac-90l This self-contained work treats the algebro-geometric and the topological aspects of Kac-Moody theory from scratch. The emphasis is on the study of the Kac-Moody groups 9 and their flag varieties XY, including their detailed construction, and their applications to the representation theory of g. In the finite case, 9 is nothing but a semisimple Y simply-connected algebraic group and X is the flag variety 9 /Py for a parabolic subgroup p y C g.
Download or read book The Arnold Gelfand Mathematical Seminars written by V. Arnold and published by Springer Science & Business Media. This book was released on 1997-02-18 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is very tempting but a little bit dangerous to compare the style of two great mathematicians or of their schools. I think that it would be better to compare papers from both schools dedicated to one area, geometry and to leave conclusions to a reader of this volume. The collaboration of these two schools is not new. One of the best mathematics journals Functional Analysis and its Applications had I.M. Gelfand as its chief editor and V.I. Arnold as vice-chief editor. Appearances in one issue of the journal presenting remarkable papers from seminars of Arnold and Gelfand always left a strong impact on all of mathematics. We hope that this volume will have a similar impact. Papers from Arnold's seminar are devoted to three important directions developed by his school: Symplectic Geometry (F. Lalonde and D. McDuff), Theory of Singularities and its applications (F. Aicardi, I. Bogaevski, M. Kazarian), Geometry of Curves and Manifolds (S. Anisov, V. Chekanov, L. Guieu, E. Mourre and V. Ovsienko, S. Gusein-Zade and S. Natanzon). A little bit outside of these areas is a very interesting paper by M. Karoubi Produit cyclique d'espaces et operations de Steenrod.
Download or read book Applications of Hypergroups and Related Measure Algebras written by and published by American Mathematical Soc.. This book was released on 1995-02-28 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: `The most important single thing about this conference was that it brought together for the first time representatives of all major groups of users of hypergroups. [They] talked to each other about how they were using hypergroups in fields as diverse as special functions, probability theory, representation theory, measure algebras, Hopf algebras, and Hecke algebras. This led to fireworks.' - from the Introduction. Hypergroups occur in a wide variety of contexts, and mathematicians the world over have been discovering this same mathematical structure hidden in very different applications. The diverse viewpoints on the subject have led to the need for a common perspective, if not a common theory. Presenting the proceedings of a Joint Summer Research Conference held in Seattle in the summer of 1993, this book will serve as a valuable starting point and reference tool for the wide range of users of hypergroups and make it easier for an even larger audience to use these structures in their work.
Download or read book Representations of Algebraic Groups written by Jens Carsten Jantzen and published by American Mathematical Soc.. This book was released on 2003-01-01 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now back in print by the AMS, this is a significantly revised edition of a book originally published in 1987 by Academic Press. This book gives the reader an introduction to the theory of algebraic representations of reductive algebraic groups. To develop appropriate techniques, the first part of the book is an introduction to the general theory of representations of algebraic group schemes. Here, the author describes important basic notions: induction functors, cohomology,quotients, Frobenius kernels, and reduction mod $p$, among others. The second part of the book is devoted to the representation theory of reductive algebraic groups. It includes topics such as the description of simple modules, vanishing theorems, the Borel-Bott-Weil theorem and Weyl's character formula, andSchubert schemes and line bundles on them. For this revised edition the author added nearly 150 pages of new material describing some later developments, among them Schur algebras, Lusztig's conjecture and Kazhdan-Lusztig polynomials, tilting modules, and representations of quantum groups. He also made major revisions to parts of the old text. Jantzen's book continues to be the ultimate source of information on representations of algebraic groups in finite characteristics. It is suitable forgraduate students and research mathematicians interested in algebraic groups and their representations.
Download or read book Multivariable Operator Theory written by Raúl E. Curto and published by American Mathematical Soc.. This book was released on 1995 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a collection of papers presented at a conference on multivariable operator theory. The articles contain contributions to a variety of areas and topics which may be viewed as forming an emerging new subject. This subject involves the study of geometric rather than topological invariants associated with the general theme of operator theory in several variables. This collection will spur further discussion among the different research groups.
Download or read book Set Theory written by Tomek Bartoszyński and published by American Mathematical Soc.. This book was released on 1996 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of papers presented at the first three meetings of the Boise Extravaganza in Set Theory (BEST) at Boise State University, Idaho, in 1992, 1993, and 1994. Articles in this volume present recent results in several areas of set theory.
Download or read book Topology and Representation Theory written by Eric M. Friedlander and published by American Mathematical Soc.. This book was released on 1994 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: During 1991-1992, Northwestern University conducted a special emphasis year on the topic, "The connections between topology and representation theory." Activities over the year culminated in a conference in May 1992 which attracted over 120 participants. Most of the plenary lectures at the conference were expository and designed to introduce current trends to graduate students and nonspecialists familiar with algebraic topology. This volume contains refereed papers presented or solicited at the conference; one paper is based on a seminar given during the emphasis year.
