Representations of Lie algebras, quantum groups, and related topics : AMS Special Session on Representations of Lie Algebras, Quantum Groups, and Related Topics, November 12-13, 2016, North Carolina State University, Raleigh, North Carolina / Naihuan Jing, Kailash C. Misra, editors.

Format:

Book

Conference/Event

Contributor:

Jing, Naihuan, editor.

Misra, Kailash C., 1954- editor.

Conference Name:

AMS Special Session on Representations of Lie Algebras, Quantum Groups, and Related Topics (2016 : Raleigh, N.C.)

Series:

Contemporary mathematics (American Mathematical Society). 0271-4132 713

Contemporary mathematics, 713 0271-4132

Language:

English

Subjects (All):

Representations of Lie algebras--Congresses.

Representations of Lie algebras.

Algebra--Congresses.

Algebra.

Physical Description:

1 online resource (242 pages).

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2018.

Summary:

This volume contains the proceedings of the AMS Special Session on Representations of Lie Algebras, Quantum Groups and Related Topics, held from November 12-13, 2016, at North Carolina State University, Raleigh, North Carolina. The articles cover various aspects of representations of Kac-Moody Lie algebras and their applications, structure of Leibniz algebras and Krichever-Novikov algebras, representations of quantum groups, and related topics.

Contents:

Cover

Title page

Contents

Preface

The two bosonizations of the CKP hierarchy: Overview and character identities

1. Introduction

2. The CKP hierarchy and its two bosonizations: overview

3. Graded dimensions and character identities

4. Appendix

References

Inhomogeneous supersymmetric bilinear forms

2. Invariants

3. Classification up to dimension 7

4. Oscillator Lie superalgebras

Acknowledgments

Imaginary crystal bases for _{ }(̂ (2))-modules in category ^{ }_{ ℯ , }

2. Quantum affine algebra _{ }(̂ (2))

3. Ω-operators and the Kashiwara algebra _{ }

4. Quantized imaginary Verma modules and category ^{ }_{ ℯ , }

5. Imaginary crystal lattice and imaginary crystal basis

On the module structure of the center of hyperelliptic Krichever-Novikov algebras

Classification of 5-dimensional complex nilpotent Leibniz algebras

2. Classification of nilpotent Leibniz algebras with dim( ²)=3 and dim( ( ))=1

3. Classification of 5-dimensional complex nilpotent Leibniz algebras

Gelfand-Tsetlin modules of (3) in the principal block

2. Gelfand-Tsetlin modules for ( )

3. Gelfand-Tsetlin modules with tableaux realization for ( )

4. Irreducible Gelfand-Tsetlin modules in the principal block

5. ₂₁-localization of Gelfand-Tsetlin modules in the principal block

Fusion rings revisited

1. Kac-Moody algebras of affine types

2. Fusion rings associated to Kac-Moody algebras of affine types

3. Twining formula and Verlinde formula

4. Proofs

5. Modular S-matrix

Kostant-Lusztig -bases of multiparameter quantum groups

1. Introduction.

2. Generalized quantum groups

3. Kostant-Lusztig \bA-form

Catalan triangle numbers and binomial coefficients

2. Catalan expansion of binomial coefficients

3. Alternating Jacobsthal triangle

4. -deformation

5. -analogue of -deformation

Walk algebras, distinguished subexpressions, and point counting in Kac-Moody flag varieties

2. Notation and preliminaries

3. Hecke algebras and walk algebras

4. Change of basis formula

5. Counting points in Kac-Moody flag varieties

6. Some connections to other work

Critical points of master functions and mKdV hierarchy of type ⁽²⁾_{2 }

2. Kac-Moody algebra of type _{2 }⁽¹⁾

3. Kac-Moody algebra of type _{2 }⁽²⁾

4. mKdV equations

5. Tangent maps to Miura maps

6. Critical points of master functions and generation of tuples of polynomials

7. Critical points of master functions and Miura opers

8. Vector fields

Back Cover.

Notes:

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-4882-3