Cohomological Tensor Functors on Representations of the General Linear Supergroup.

Format:

Book

Author/Creator:

Heidersdorf, Thorsten.

Contributor:

Weissauer, Rainer.

Series:

Memoirs of the American Mathematical Society

Memoirs of the American Mathematical Society ; v.270

Language:

English

Subjects (All):

Tensor algebra.

Tensor products.

Physical Description:

1 online resource (118 pages)

Edition:

1st ed.

Place of Publication:

Providence : American Mathematical Society, 2021.

Summary:

"We define and study cohomological tensor functors from the category Tn of finite-dimensional representations of the supergroup for the image of an arbitrary irreducible representation. In particular DS(L) is semisimple and multiplicity free. We derive a few applications of this theorem such as the degeneration of certain spectral sequences and a formula for the modified superdimension of an irreducible representation"-- Provided by publisher.

Contents:

Cover

Title page

Chapter 1. Introduction

Chapter 2. Cohomological Tensor Functors

2.1. The superlinear groups

2.2. The Duflo-Serganova functor

2.3. Cohomology functors

2.4. Support varieties and the kernel of

2.5. The tensor functor

2.6. The relation between ( ) and ( )

2.7. Hodge decomposition

2.8. The case &gt

1

2.9. Boundary maps

2.10. Highest weight modules

2.11. The Casimir

Chapter 3. The Main Theorem and its Proof

3.1. The language of Brundan and Stroppel

3.2. On segments, sectors and plots

3.3. Mixed tensors and ground states

3.4. Sign normalizations

3.5. The main theorem

3.6. Strategy of the proof

3.7. Modules of Loewy length 3

3.8. Inductive Control over

3.9. Moves

Chapter 4. Consequences of the Main Theorem

4.1. Tannaka Duals

4.2. Cohomology I

4.3. Cohomology II

4.4. Cohomology III

4.5. The forest formula

4.6. -module structure on the cohomology ^{∙}_{ _{ }}

4.7. Primitive elements of ^{∙}_{ _{ }}( (1))

4.8. Kac module of 1

4.9. Strict morphisms

4.10. The module (( )ⁿ)

4.11. The basic hook representations

Bibliography

Back Cover.

Notes:

Description based on publisher supplied metadata and other sources.

Includes bibliographical references.

ISBN:

9781470465285

1470465280

OCLC:

1259594040