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Geometric Representation Theory and Extended Affine Lie Algebras

Edited by: Erhard Neher University of Ottawa, Ottawa, ON, Canada
Alistair Savage University of Ottawa, Ottawa, ON, Canada
Weiqiang Wang University of Virginia, Charlottesville, VA
A co-publication of the AMS and Fields Institute
Available Formats:
Hardcover ISBN: 978-0-8218-5237-8
Product Code: FIC/59
List Price: $111.00 MAA Member Price:$99.90
AMS Member Price: $88.80 Electronic ISBN: 978-1-4704-1785-7 Product Code: FIC/59.E List Price:$104.00
MAA Member Price: $93.60 AMS Member Price:$83.20
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List Price: $166.50 MAA Member Price:$149.85
AMS Member Price: $133.20 Click above image for expanded view Geometric Representation Theory and Extended Affine Lie Algebras Edited by: Erhard Neher University of Ottawa, Ottawa, ON, Canada Alistair Savage University of Ottawa, Ottawa, ON, Canada Weiqiang Wang University of Virginia, Charlottesville, VA A co-publication of the AMS and Fields Institute Available Formats:  Hardcover ISBN: 978-0-8218-5237-8 Product Code: FIC/59  List Price:$111.00 MAA Member Price: $99.90 AMS Member Price:$88.80
 Electronic ISBN: 978-1-4704-1785-7 Product Code: FIC/59.E
 List Price: $104.00 MAA Member Price:$93.60 AMS Member Price: $83.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$166.50 MAA Member Price: $149.85 AMS Member Price:$133.20
• Book Details

Fields Institute Communications
Volume: 592011; 213 pp
MSC: Primary 16; 17;

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.

Graduate students and research mathematicians interested in Lie algebras and algebraic combinatorics.

• Chapters
• Joel Kamnitzer - Geometric constructions of the irreducible representations of $GL_n$
• Seok-Jin Kang - Introduction to crystal bases
• Alistair Savage - Geometric realizations of crystals
• Weiqiang Wang - Nilpotent orbits and finite $W$-algebras
• Erhard Neher - Extended affine Lie algebras—An introduction to their structure theory
• Vyjayanthi Chari - Representations of affine and toroidal Lie algebras

• Requests

Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
Volume: 592011; 213 pp
MSC: Primary 16; 17;

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.

Graduate students and research mathematicians interested in Lie algebras and algebraic combinatorics.

• Chapters
• Joel Kamnitzer - Geometric constructions of the irreducible representations of $GL_n$
• Seok-Jin Kang - Introduction to crystal bases
• Alistair Savage - Geometric realizations of crystals
• Weiqiang Wang - Nilpotent orbits and finite $W$-algebras
• Erhard Neher - Extended affine Lie algebras—An introduction to their structure theory
• Vyjayanthi Chari - Representations of affine and toroidal Lie algebras
Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
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