On the one-dimensional representations of the general linear supergroup

2010/03/12 by I. M. Trishin, Trishin, I. M.
Mathematics · #20G05 #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:20G05

paper · pdf · doi:10.48550/arxiv.1003.2490

34 pages, 2 figures

arxiv created 2010/03/12 · arxiv updated 2010/03/15

Abstract

Because of its multiplicativity, the Berezinian is the character of the one-dimensional representation of the general linear supergroup. We give an explicit construction of this representation on a space of tensors. Similarly, we construct the representation such that its character is the inverse of the Berezinian.

Related

• Tensor Representations of the General Linear Supergroup
• Berezin quantization and representation theory
• Deligne's category Rep(GL_δ) and representations of general linear supergroups
• Berezin symbols on Lie groups
• Representation Theory of General Linear Supergroups in Characteristic 2