Open AccessDeligne’s category \underline{𝑅𝑒}𝑝(𝐺𝐿_{𝛿}) and representations of general linear supergroups
Author(s) -
Jonathan Comes,
Benjamin Wilson
Publication year - 2012
Publication title -
representation theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.169
H-Index - 37
ISSN - 1088-4165
DOI - 10.1090/s1088-4165-2012-00425-3
Subject(s) - indecomposable module , isomorphism (crystallography) , mathematics , algorithm , artificial intelligence , computer science , crystallography , combinatorics , chemistry , crystal structure
We classify indecomposable summands of mixed tensor powers of the natural representation for the general linear supergroup up to isomorphism. We also give a formula for the characters of these summands in terms of composite supersymmetric Schur polynomials, and give a method for decomposing their tensor products. Along the way, we describe indecomposable objects in Re _ p ( G L δ ) \underline {\operatorname {Re}}\!\operatorname {p}(GL_\delta ) and explain how to decompose their tensor products.