Stacks in Representation Theory. What is a continuous representation of an algebraic group ?
Representation Theory
2016-05-13 v3
Abstract
In this note I introduce a new approach to (or rather a new language for) representation theory of groups. Namely, I propose to consider a (complex) representation of a group as a sheaf on some geometric object (a stack). This point of view necessarily leads to a conclusion that the standard approach to (continuous) representations of algebraic groups is ideologically inconsistent. I propose a way to modify this approach using sheaves on stacks. In new version I corrected some misprints and added an explanation how stack's approach is related to Vogan's picture of representations.
Keywords
Cite
@article{arxiv.1410.0435,
title = {Stacks in Representation Theory. What is a continuous representation of an algebraic group ?},
author = {Joseph Bernstein},
journal= {arXiv preprint arXiv:1410.0435},
year = {2016}
}