Perspectives in representation theory : a conference in honor of Igor Frenkel's 60th birthday : May 12-17, 2012, Yale University, New Haven, CT / Pavel Etingof, Mikhail Khovanov, Alistair Savage, editors.

Format:

Book

Contributor:

Etingof, P. I. (Pavel I.), 1969- editor.

Khovanov, Mikhail, editor.

Savage, Alistair, editor.

Frenkel, Igor, honoree.

Series:

Contemporary mathematics (American Mathematical Society). 0271-4132 610

Contemporary mathematics, 1098-3627 ; 610 0271-4132

Language:

English

Subjects (All):

Frenkel, Igor--Congresses.

Frenkel, Igor.

Representations of algebras--Congresses.

Representations of algebras.

Lie algebras--Congresses.

Lie algebras.

Representations of groups--Congresses.

Representations of groups.

Group theory--Congresses.

Group theory.

Physical Description:

1 online resource (384 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2014.

Language Note:

English

Summary:

This volume contains the proceedings of the conference Perspectives in Representation Theory, held from May 12-17, 2012, at Yale University, in honour of Igor Frenkel's 60th birthday. The aim of the conference was to present current progress on the following (interrelated) topics: vertex operator algebras and chiral algebras, conformal field theory, the (geometric) Langlands programme, affine Lie algebras, Kac-Moody algebras, quantum groups, crystal bases and canonical bases, quantum cohomology and K-theory, geometric representation theory, categorification, higher-dimensional Kac-Moody theory, integrable systems, quiver varieties, representations of real and p -adic groups, quantum gauge theories. The papers in this volume present representation theory connections of numerous other subjects, as well as some of the most recent advances in representation theory, including those which occurred thanks to the application of techniques in other areas of mathematics, and of ideas of quantum field theory and string theory.

Contents:

Preface

On the work of Igor Frenkel

Introduction by Pavel Etingof

1. Representation theory of affine Lie algebras by Alistair Savage and Anthony Licata

2. Quantum Knizhnik-Zamolodchikov equations by Pavel Etingof

3. Double loop groups by Pavel Etingof

4. Vertex operator algebras by John Duncan

5. Three-dimensional quantum gravity by John Duncan

6. Quaternionic analysis by Matvei Libine

7. Emergence of a new area "elliptic hypergeometric series by Michael Schlosser

8. Representation theory of split real quantum groups and modular doubles by Ivan Ip

9. Categorification by Mikhail Khovanov

10. Geometric representation theory by Anthony Licata

References

Macdonald polynomials, Laumon spaces and perverse coherent sheaves

1. Introduction

2. Combinatorial notations

3. Macdonald function

4. Vanishing

5. Parabolic Laumon spaces

6. Euler characteristics of twisted De Rham complexes

7. Difference equations

8. Speculations for arbitrary simple groups

Acknowledgments

An affine Gindikin-Karpelevich formula

2. Affine Kac-Moody groups

3. Finiteness of the Gindikin-Karpelevich Sum, Part I

4. Completion of â?»

5. Finiteness of the Gindikin-Karpelevich Sum, Part 2

6. Proof of Theorem 1.9 and Theorem 1.13

7. Appendix: Proof of 5.9

Acknowledgements

On the discrete groups of Mathieu Moonshine

2. Preliminaries

3. Cusp forms

4. Perspectives

Appendix A. Special functions

The classical master equation

2. Graded varieties

3. Solutions of the classical master equation

4. Existence and uniqueness for affine varieties

5. Computing the BRST cohomology

6. Examples

7. BRST cohomology in degree 0 and 1 and Lie"Rinehart cohomology

8. The case of quasi-projective varieties

Appendix A. Stable isomorphism of Tate resolutions

Appendix B. Gluing sheaves of differential graded algebra

DG indschemes

Introduction

1. DG indschemes

2. Sheaves on DG indschemes

4. Fourth order differential equations.

Notes:

Description based upon print version of record.

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-1523-2