The Kazhdan-Lusztig Cells in Certain Affine Weyl Groups
Author: Jian-Yi Shi
Publisher: Springer
Published: 2006-11-14
Total Pages: 318
ISBN-13: 3540397809
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Kazhdan-Lusztig Cells with Unequal Parameters
Author: Cédric Bonnafé
Publisher: Springer
Published: 2018-05-07
Total Pages: 350
ISBN-13: 3319707361
DOWNLOAD EBOOKThis monograph provides a comprehensive introduction to the Kazhdan-Lusztig theory of cells in the broader context of the unequal parameter case. Serving as a useful reference, the present volume offers a synthesis of significant advances made since Lusztig’s seminal work on the subject was published in 2002. The focus lies on the combinatorics of the partition into cells for general Coxeter groups, with special attention given to induction methods, cellular maps and the role of Lusztig's conjectures. Using only algebraic and combinatorial methods, the author carefully develops proofs, discusses open conjectures, and presents recent research, including a chapter on the action of the cactus group. Kazhdan-Lusztig Cells with Unequal Parameters will appeal to graduate students and researchers interested in related subject areas, such as Lie theory, representation theory, and combinatorics of Coxeter groups. Useful examples and various exercises make this book suitable for self-study and use alongside lecture courses. Information for readers: The character {\mathbb{Z}} has been corrupted in the print edition of this book and appears incorrectly with a diagonal line running through the symbol.
Kazhdan-Lusztig Cells in Affine Weyl Groups with Unequal Parameters
Author: Jérémie Guilhot
Publisher:
Published: 2008
Total Pages: 120
ISBN-13:
DOWNLOAD EBOOKHecke algebras arise naturally in the representation theory of reductive groups over finite or p-adic fields. These algebras are specializations of Iwahori-Hecke algebras which can be defined in terms of a Coxeter group and a weight function without reference to reductive groups and this is the setting we are working in. Kazhdan-Lusztig cells play a crucial role in the study of Iwahori-Hecke algebras. The aim of this work is to study the Kazhdan-Lusztig cells in affine Weyl groups with unequal parameters. More precisely, we show that the Kazhdan-Lusztig polynomials of an affine Weyl group are invariant under ``long enough'' translations, we decompose the lowest two-sided cell into left cells and we determine the decomposition of the affine Weyl group of type G into cells for a whole class of weight functions.
The Based Ring of Two-Sided Cells of Affine Weyl Groups of Type $\widetilde {A}_{n-1}$
Author: Nanhua Xi
Publisher: American Mathematical Soc.
Published: 2002
Total Pages: 114
ISBN-13: 0821828916
DOWNLOAD EBOOKIn this paper we prove Lusztig's conjecture on based ring for an affine Weyl group of type $\tilde A_{n-1}$.
Trends in Representation Theory of Algebras and Related Topics
Author: Andrzej Skowroński
Publisher: European Mathematical Society
Published: 2008
Total Pages: 732
ISBN-13: 9783037190623
DOWNLOAD EBOOKThis book is concerned with recent trends in the representation theory of algebras and its exciting interaction with geometry, topology, commutative algebra, Lie algebras, quantum groups, homological algebra, invariant theory, combinatorics, model theory and theoretical physics. The collection of articles, written by leading researchers in the field, is conceived as a sort of handbook providing easy access to the present state of knowledge and stimulating further development. The topics under discussion include diagram algebras, Brauer algebras, cellular algebras, quasi-hereditary algebras, Hall algebras, Hecke algebras, symplectic reflection algebras, Cherednik algebras, Kashiwara crystals, Fock spaces, preprojective algebras, cluster algebras, rank varieties, varieties of algebras and modules, moduli of representations of quivers, semi-invariants of quivers, Cohen-Macaulay modules, singularities, coherent sheaves, derived categories, spectral representation theory, Coxeter polynomials, Auslander-Reiten theory, Calabi-Yau triangulated categories, Poincare duality spaces, selfinjective algebras, periodic algebras, stable module categories, Hochschild cohomologies, deformations of algebras, Galois coverings of algebras, tilting theory, algebras of small homological dimensions, representation types of algebras, and model theory. This book consists of fifteen self-contained expository survey articles and is addressed to researchers and graduate students in algebra as well as a broader mathematical community. They contain a large number of open problems and give new perspectives for research in the field.
Group Theory in China
Author: Zhexian Wan
Publisher: Springer Science & Business Media
Published: 1996
Total Pages: 282
ISBN-13: 9780792339892
DOWNLOAD EBOOKHsio-Fu Tuan is a Chinese mathematician who has made important contributions to the theories of both finite groups and Lie groups. He has also had a great influence on the development of algebra, and particularly group theory in China. The present volume consists of a collection of essays on various aspects of group theory written by some of his former students and colleagues in honour of his 80th birthday. The papers contain the main general results, as well as recent ones, on certain topics within this discipline. The chief editor, Zhe-Xian Wan, is a leading algebraist in China.
Kazhdan-Lusztig Polynomials and Cells for Affine Weyl Groups and Unequal Parameters
Author: Kirsten Bremke
Publisher:
Published: 1996
Total Pages: 74
ISBN-13:
DOWNLOAD EBOOKCombinatorics of Coxeter Groups
Author: Anders Bjorner
Publisher: Springer Science & Business Media
Published: 2006-02-25
Total Pages: 371
ISBN-13: 3540275967
DOWNLOAD EBOOKIncludes a rich variety of exercises to accompany the exposition of Coxeter groups Coxeter groups have already been exposited from algebraic and geometric perspectives, but this book will be presenting the combinatorial aspects of Coxeter groups
The Based Ring of Two-sided Cells of Affine Weyl Groups of Type Ìn_-_1_
Author: Nanhua Xi
Publisher: American Mathematical Soc.
Published: 2002-03-19
Total Pages: 116
ISBN-13: 9780821864715
DOWNLOAD EBOOKIn this paper we prove Lusztig's conjecture on based ring for an affine Weyl group of type $\tilde A_{n-1}$.
Representations of Algebraic Groups, Quantum Groups, and Lie Algebras
Author: Georgia Benkart
Publisher: American Mathematical Soc.
Published: 2006
Total Pages: 270
ISBN-13: 0821839241
DOWNLOAD EBOOKCovers various aspects of the representation theory of Lie algebras, finite groups of Lie types, Hecke algebras, and Lie super algebras. This book outlines connections among irreducible representations of certain blocks of reduced enveloping algebras of semi-simple Lie algebras in positive characteristic.
