**Fields Institute Communications**

Volume: 59;
2011;
213 pp;
Hardcover

MSC: Primary 16; 17;

Print ISBN: 978-0-8218-5237-8

Product Code: FIC/59

List Price: $104.00

AMS Member Price: $83.20

MAA Member Price: $93.60

**Electronic ISBN: 978-1-4704-1785-7
Product Code: FIC/59.E**

List Price: $104.00

AMS Member Price: $83.20

MAA Member Price: $93.60

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# Geometric Representation Theory and Extended Affine Lie Algebras

Share this page *Edited by *
*Erhard Neher; Alistair Savage; Weiqiang Wang*

A co-publication of the AMS and Fields Institute

Lie theory has connections to many other disciplines such as geometry,
number theory, mathematical physics, and algebraic combinatorics. The
interaction between algebra, geometry and combinatorics has proven to be
extremely powerful in shedding new light on each of these areas.

This book presents the lectures given at the Fields Institute
Summer School on Geometric Representation Theory and Extended Affine
Lie Algebras held at the University of Ottawa in 2009. It provides a
systematic account by experts of some of the exciting developments in
Lie algebras and representation theory in the last two decades. It
includes topics such as geometric realizations of irreducible
representations in three different approaches, combinatorics and
geometry of canonical and crystal bases, finite \(W\)-algebras
arising as the quantization of the transversal slice to a nilpotent
orbit, structure theory of extended affine Lie algebras, and
representation theory of affine Lie algebras at level zero.

This book will be of interest to mathematicians working in Lie
algebras and to graduate students interested in learning the basic
ideas of some very active research directions. The extensive
references in the book will be helpful to guide non-experts to the
original sources.

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 Lie algebras and algebraic combinatorics.

# Table of Contents

## Geometric Representation Theory and Extended Affine Lie Algebras

- Cover Cover11
- Title page i2
- Contents iii4
- Preface v6
- Geometric constructions of the irreducible representations of 𝐺𝐿_{𝑛} 110
- Introduction to crystal bases 1928
- Geometric realizations of crystals 4554
- Nilpotent orbits and finite 𝑊-algebras 7180
- Extended affine Lie algebras—An introduction to their structure theory 107116
- Representations of affine and toroidal Lie algebras 169178
- Bibliography 199208
- Index 209218
- Back Cover Back Cover1226