Lie Groups, Number Theory, and Vertex Algebras.

Format:

Book

Author/Creator:

Adamović, Dražen.

Contributor:

Dujella, Andrej.

Milas, Antun.

Series:

Contemporary Mathematics

Contemporary Mathematics ; v.768

Language:

English

Subjects (All):

Representations of groups--Congresses.

Representations of groups.

Representations of algebras--Congresses.

Representations of algebras.

Physical Description:

1 online resource (356 pages)

Edition:

1st ed.

Other Title:

Lie groups, number theory, and vertex algebras

Place of Publication:

Providence : American Mathematical Society, 2021.

Summary:

This volume contains the proceedings of the conference Representation Theory XVI, held from June 25-29, 2019, in Dubrovnik, Croatia.The articles in the volume address selected aspects of representation theory of reductive Lie groups and vertex algebras, and are written by prominent experts in the field as well as junior researchers. The three main topics of these articles are Lie theory, number theory, and vertex algebras.

Contents:

Cover

Title page

Contents

Preface

Group photo of the participants

Lie groups

The Racah algebra: An overview and recent results

1. Introduction

2. The higher rank Racah algebra

3. The Racah problem for (1,1) and multivariate Racah polynomials

4. Realizations of the higher rank Racah algebra

5. Further results and conclusions

References

Orbit embedding for double flag varieties and Steinberg maps

Introduction

1. Steinberg theory for symmetric pairs: A review

2. Combinatorial Steinberg maps

3. Embedding of the orbits in double flag varieties

4. Steinberg theory for type CI embedded into type AIII

Acknowledgments

Symplectic Dirac cohomology and lifting of characters to metaplectic groups

2. Preliminaries on symplectic Dirac cohomology for Lie superalgebras

3. Rittenberg-Scheunert correspondence

4. Lifting of characters to metaplectic groups

Spectrum of semisimple locally symmetric spaces and admissibility of spherical representations

2. Existence of compact Clifford-Klein forms and spherical triples

3. -admissibility

4. Embedding of Casimir operators

5. On the spectrum _{ ²(Γ\ / )}( ( / ))

6. Generalized matrix coefficients, unitarity and continuous spectrum

Four examples of Beilinson-Bernstein localization

2. Set-up

3. Serre's twisting sheaves

4. Twisted sheaves of differential operators

5. Finite dimensional modules

6. Verma modules

7. Admissible representations of \SL(2,ℝ)

8. Whittaker modules

Number theory

Perfect powers in polynomial power sums

2. Results

3. Preliminaries

4. Proofs

References.

The number of irregular Diophantine quadruples for a fixed Diophantine pair or triple

2. Proofs of Theorems 1.2 and 1.3

3. Proof of Theorem 1.4

4. Proofs of Theorems 1.6 and 1.7

On ideals defining irreducible representations of reductive -adic groups

2. Elementary properties of Hecke algebras and ideals

3. Bernstein center

4. The proof of Theorem 1.2

5. Computation of certain Jacquet modules and Proof of Proposition 1.5

On diophantine properties of radix representations in algebraic number fields

2. Periodic -integers

3. Periodic rational integers

4. Rational integers with fixed representation word

5. Repunits in number systems

Vertex algebras

On certain -algebras of type _{ }( ₄, )

2. Affine -algebras

3. The collapsing level =-8/3

4. The level =-5/2 and a certain Heisenberg coset

5. Case =-7/3

On the =1 super Heisenberg-Virasoro vertex algebra

2. Preliminaries

3. Heisenberg-Virasoro vertex algebra

4. Definition of the =1 Heisenberg-Virasoro vertex algebra

5. Realization at non-zero level

6. Realization at level zero

7. Determinant formula

Character rings and fusion algebras

2. FC sets and their classes

3. Central extensions

4. Local s

5. Summary

Continuing Remarks on the Unrolled Quantum Group of (2)

2. The unrolled quantum group and its associated category

3. The center of \overline{ }_{ }^{ }( ₂)

4. Simple and projective modules of

5. Projective covers, resolutions, and extensions of _{ }⊗ℂ^{ℍ}_{ ℓ}

6. Logarithmic typical modules.

References

On the geometric interpretation of certain vertex algebras and their modules

1. Overview

2. Formal geometry

3. Vertex algebras and their modules

4. The geometric interpretation of the vertex algebra _{ } and its modules

Representation theory of vertex operator algebras and orbifold conformal field theory

2. A program to construct conformal field theories

3. Basic open problems and conjectures in orbifold conformal field theory

4. Twisted modules, a general construction and existence results

5. Twisted intertwining operators

6. Main conjectural properties of twisted intertwining operators

7. Some thoughts on further developments

Further -series identities and conjectures relating false theta functions and characters

1. Introduction and previous work

2. Quantum dilogarithm

3. Bailey's lemma and other known -series identities

4. Identities with half-characteristic

5. Identities for characters

6. Identities for Nahm-type sums with higher order poles

7. Relations with sum of tails identities

8. Principal subspaces and infinite jet schemes

9. Final comments

Ultra-discretization of ₆⁽¹⁾- geometric crystal at the spin node

2. Perfect crystals of type ₆⁽¹⁾

3. Ultra-discretization of ( ₆⁽¹⁾)

Twisted exterior derivative for universal enveloping algebras

1. Preliminaries and basic notation

2. The twisted algebra of differential forms

3. Exterior derivative

The Heisenberg generalized vertex operator algebra on a Riemann surface

2. Some generalized MacMahon master theorems

3. Riemann surfaces from a sewn sphere

4. The Heisenberg vertex operator algebra on _{ℊ}.

5. The Heisenberg generalized VOA on _{ℊ}

6. Appendix

Back Cover.

Notes:

Description based on publisher supplied metadata and other sources.

Includes bibliographical references.

ISBN:

9781470464240

1470464241

OCLC:

1256237658