Lie algebras, vertex operator algebras, and related topics : a conference in honor of J. Lepowsky and R. Wilson, August 14-18, 2015, University of Notre Dame, Notre Dame, Indiana / Katrina Barron [and three others], editors.

Format:

Book

Contributor:

Barron, Katrina, 1965- editor.

Lepowsky, J. (James), honoree.

Wilson, Robert L., 1946- honoree.

Series:

Contemporary mathematics (American Mathematical Society). 0271-4132 695

Contemporary mathematics, 695 0271-4132

Language:

English

Subjects (All):

Lepowsky, J. (James).

Lepowsky, J.

Wilson, Robert L., 1946-.

Wilson, Robert L.

Lie algebras--Congresses.

Lie algebras.

Vertex operator algebras--Congresses.

Vertex operator algebras.

Representations of algebras--Congresses.

Representations of algebras.

Physical Description:

1 online resource (282 pages) : illustrations.

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2017.

Summary:

This volume contains the proceedings of the conference on Lie Algebras, Vertex Operator Algebras, and Related Topics, celebrating the 70th birthday of James Lepowsky and Robert Wilson, held from August 14-18, 2015, at the University of Notre Dame, Notre Dame, Indiana. Since their seminal work in the 1970s, Lepowsky and Wilson, their collaborators, their students, and those inspired by their work, have developed an amazing body of work intertwining the fields of Lie algebras, vertex algebras, number theory, theoretical physics, quantum groups, the representation theory of finite simple groups, and more. The papers presented here include recent results and descriptions of ongoing research initiatives representing the broad influence and deep connections brought about by the work of Lepowsky and Wilson and include a contribution by Yi-Zhi Huang summarizing some major open problems in these areas, in particular as they pertain to two-dimensional conformal field theory.

Contents:

Cover

Title page

Contents

Preface

Generalizations of -systems and orthogonal polynomials from representation theory

1. Introduction

2. Calculating ̂ ₂ Tau-Functions on Two-Component Fermionic Fock Space

3. Generalizing to ̂ ₃

4. Connection Matrices and Zero Curvature Equations

5. Orthogonal Polynomials from Connection Matrices

References

Some applications and constructions of intertwining operators in Logarithmic Conformal Field Theory

2. Classification of irreducible modules for orbifold \triplet^{ _{ }}: A fusion rules approach

3. Fusion rules for \singlet and a proof of Conjecture 2.3 for =2.

4. Deformed realization of the triplet and singlet vertex algebra

5. Intertwining operators between typical \singlet and \triplet^{ _{ }}-modules: the =2 case

Acknowledgments

Kac-Moody groups and automorphic forms in low dimensional supergravity theories

2. Supergravity theories

3. Construction of Kac-Moody groups over \R and \Z

4. Eisenstein series in supergravity

5. Eisenstein series on non-affine Kac-Moody groups

6. Some open questions

The Lusztig-Macdonald-Wall polynomial conjectures and -difference equations

1. Introduction and statement of results

2. Hypergeometric -series and proofs of results

3. The LMW polynomials and the affine Lie algebra ̂\frak{ }₂

Uniqueness of representation-theoretic hyperbolic Kac-Moody groups over ℤ

2. Tits' Kac-Moody group

3. Tits' presentation

4. Simply laced hyperbolic type

5. Finitely many defining relations parametrized over

6. Representation-theoretic Kac-Moody groups over rings

7. Uniqueness of representation-theoretic Kac-Moody groups over \Z

8. The kernel of _{ }

Acknowledgement

References.

Coends in conformal field theory

1. Coends in mathematics and physics

2. Some facts about specific coends

3. Coends in functor categories

4. Fubini theorems

Remarks on -coordinated modules for quantum vertex algebras

2. -coordinated modules for weak quantum vertex algebras

3. -coordinated module ( ( ), _{ }*)

The classification of chiral WZW models by ⁴₊( ,ℤ)

2. Geometric quantization

3. ⁴( ) for connected Lie groups

4. Representations of affine and Heisenberg VOAs

5. Simple current extensions

6. The minimal energy

7. The classification of chiral WZW models

8. WZW conformal nets

9. Conclusion

Some open problems in mathematical two-dimensional conformal field theory

2. The construction of rational conformal field theories satisfying the axioms of Kontsevich-Segal-Moore-Seiberg

3. Cohomology theory for graded vertex algebras and complete reducibility of their modules

4. The moduli space of conformal field theories

5. The construction and study of logarithmic conformal field theories

6. Orbifold conformal field theories

7. The uniqueness of the moonshine module vertex operator algebra and the classification of meromorphic rational conformal field theories of central charge 24

8. Calabi-Yau superconformal field theories

9. The relation between the approaches of vertex operator algebras and conformal nets

On realization of some twisted toroidal Lie algebras

2. Twisted Toroidal Lie Algebras

3. MRY presentation of (\g)

Twisted generating functions incorporating singular vectors in Verma modules and their localizations, I

2. Twisted generating functions for singular vectors in Verma modules for (2).

3. Localization of ( ) and of Verma modules

4. Twisted generating functions for singular vectors in the modules of fractions

Characterization of the simple Virasoro vertex operator algebras with 2 and 3-dimensional space of characters

Introduction

1. Overview

2. Special cases of the Kaneko-Zagier equations

3. 3rd order modular linear differential equations

4. Diophantus equation, central charges and conformal weights

5. Condition for modules

6. Characterization of the minimal models

7. Appendix

Quasiconformal Teichmüller theory as an analytical foundation for two-dimensional conformal field theory

2. Conformal field theory

3. Quasiconformal mappings and \teich theory

4. Teichmüller space/rigged moduli space correspondence

5. Analytic setting for the determinant line bundle

6. Summary: why Weil-Petersson class riggings?

Centralizing the centralizers

2. Spin chains for _{ } Nichols algebras

3. Commuting families: Jucys-Murphy elements

4. Commuting families from Baxterization

5. Outlook

On Neeman's gradient flows

2. Some gradient systems

3. The Neeman flow (as explained by Gerry Schwarz)

4. Neeman's theorem.

5. An elementary result

6. Neeman's argument for Tori

Back Cover.

Notes:

Includes bibliographical references at the end of each chapters.

Description based on print version record.

ISBN:

1-4704-4196-9