**Fields Institute Communications**

Volume: 40;
2004;
479 pp;
Hardcover

MSC: Primary 16; 17; 14;
Secondary 05; 13; 15; 18; 20; 51; 81

Print ISBN: 978-0-8218-3416-9

Product Code: FIC/40

List Price: $138.00

Individual Member Price: $110.40

**Electronic ISBN: 978-1-4704-3074-0
Product Code: FIC/40.E**

List Price: $138.00

Individual Member Price: $110.40

# Representations of Finite Dimensional Algebras and Related Topics in Lie Theory and Geometry

Share this page *Edited by *
*Vlastimil Dlab; Claus Michael Ringel*

A co-publication of the AMS and Fields Institute

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.

Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

#### Readership

Graduate students and research mathematicians interested in representations of finite-dimensional algebras and applications.

# Table of Contents

## Representations of Finite Dimensional Algebras and Related Topics in Lie Theory and Geometry

- Cover Cover11
- Title page i2
- Contents iii4
- Preface v6
- Schedule of talks vii8
- List of participants xi12
- Instructional Workshop 120
- Semigroup and ring theoretical methods in probability 322
- Typical examples of tame algebras 2746
- Representation dimension and Solomon zeta function 4564
- Filtrations, stratifications and applications 6584
- Bruhat-Renner decomposition and Hecke algebras of reductive monoids 113132
- Representations and blocks of algebraic monoids 125144
- The descent algebra of the symmetric group 145164
- Specialized Workshop Commutative Algebra, Algebraic Geometry and Representation Theory 163182
- A remark on Letzter–Makar-Limanov invariants 165184
- Derived categories of coherent sheaves on rational singular curves 173192
- Vector bundles and Cohen-Macaulay modules 189208
- Specialized Workshop Finite Dimensional Algebras, Algebraic Groups and Lie Theory 223242
- Finite dimensional algebras, quantum groups and finite groups of Lie type 225244
- Stratified algebras arising in Lie theory 245264
- Character formulas of Kazhdan-Lusztig type 261280
- Weight theory in the context of arbitrary finite groups 277296
- Specialized Workshop Quantum Groups and Hall Algebras 291310
- Restricted two-parameter quantum groups 293312
- On Ringel-Hall algebras 319338
- Lusztig’s geometric approach to Hall algebras 349368
- The use of geometric and quantum group techniques for wild quivers 365384
- An introduction to perverse sheaves 391410
- An introduction to canonical bases 431450
- Quivers of type 𝐴, flag varieties and representation theory 453472
- Back Cover Back Cover1502