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Hardcover ISBN:  9780821834169 
Product Code:  FIC/40 
List Price:  $155.00 
MAA Member Price:  $139.50 
AMS Member Price:  $124.00 
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Product Code:  FIC/40.E 
List Price:  $145.00 
MAA Member Price:  $130.50 
AMS Member Price:  $116.00 
Hardcover ISBN:  9780821834169 
eBook ISBN:  9781470430740 
Product Code:  FIC/40.B 
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Book DetailsFields Institute CommunicationsVolume: 40; 2004; 479 ppMSC: Primary 16; 17; 14; Secondary 05; 13; 15; 18; 20; 51; 81;
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 CohenMacaulay 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 copublished with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
ReadershipGraduate students and research mathematicians interested in representations of finitedimensional algebras and applications.

Table of Contents

Instructional Workshop

Kenneth Brown — Semigroup and ring theoretical methods in probability

Thomas Bruestle — Typical examples of tame algebras

Osamu Iyama — Representation dimension and Solomon zeta function

Steffen Koenig — Filtrations, stratifications and applications

Mohan Putcha — BruhatRenner decomposition and Hecke algebras of reductive monoids

Lex Renner — Representations and blocks of algebraic monoids

Manfred Schocker — The descent algebra of the symmetric group

Specialized Workshop Commutative Algebra, Algebraic Geometry and Representation Theory

Yuri Berest — A remark on Letzter–MakarLimanov invariants

Igor Burban — Derived categories of coherent sheaves on rational singular curves

Yuriy Drozd — Vector bundles and CohenMacaulay modules

Specialized Workshop Finite Dimensional Algebras, Algebraic Groups and Lie Theory

Jie Du — Finite dimensional algebras, quantum groups and finite groups of Lie type

Volodymyr Mazorchuk — Stratified algebras arising in Lie theory

Toshiyuki Tanisaki — Character formulas of KazhdanLusztig type

Peter Webb — Weight theory in the context of arbitrary finite groups

Specialized Workshop Quantum Groups and Hall Algebras

Georgia Benkart and Sarah Witherspoon — Restricted twoparameter quantum groups

Bangming Deng and Jie Xiao — On RingelHall algebras

Zongzhu Lin — Lusztig’s geometric approach to Hall algebras

Markus Reineke — The use of geometric and quantum group techniques for wild quivers

Konstanze Rietsch — An introduction to perverse sheaves

Yoshihisa Saito — An introduction to canonical bases

Olivier Schiffmann — Quivers of type $A$, flag varieties and representation theory


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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 CohenMacaulay 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 copublished with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
Graduate students and research mathematicians interested in representations of finitedimensional algebras and applications.

Instructional Workshop

Kenneth Brown — Semigroup and ring theoretical methods in probability

Thomas Bruestle — Typical examples of tame algebras

Osamu Iyama — Representation dimension and Solomon zeta function

Steffen Koenig — Filtrations, stratifications and applications

Mohan Putcha — BruhatRenner decomposition and Hecke algebras of reductive monoids

Lex Renner — Representations and blocks of algebraic monoids

Manfred Schocker — The descent algebra of the symmetric group

Specialized Workshop Commutative Algebra, Algebraic Geometry and Representation Theory

Yuri Berest — A remark on Letzter–MakarLimanov invariants

Igor Burban — Derived categories of coherent sheaves on rational singular curves

Yuriy Drozd — Vector bundles and CohenMacaulay modules

Specialized Workshop Finite Dimensional Algebras, Algebraic Groups and Lie Theory

Jie Du — Finite dimensional algebras, quantum groups and finite groups of Lie type

Volodymyr Mazorchuk — Stratified algebras arising in Lie theory

Toshiyuki Tanisaki — Character formulas of KazhdanLusztig type

Peter Webb — Weight theory in the context of arbitrary finite groups

Specialized Workshop Quantum Groups and Hall Algebras

Georgia Benkart and Sarah Witherspoon — Restricted twoparameter quantum groups

Bangming Deng and Jie Xiao — On RingelHall algebras

Zongzhu Lin — Lusztig’s geometric approach to Hall algebras

Markus Reineke — The use of geometric and quantum group techniques for wild quivers

Konstanze Rietsch — An introduction to perverse sheaves

Yoshihisa Saito — An introduction to canonical bases

Olivier Schiffmann — Quivers of type $A$, flag varieties and representation theory