Semisimple super Tannakian categories with a small tensor generator

Thomas Krämer and Rainer Weissauer

Vol. 276 (2015), No. 1, 229–248

DOI: 10.2140/pjm.2015.276.229

Abstract

We consider semisimple super Tannakian categories generated by an object whose symmetric or alternating tensor square is simple up to trivial summands. Using representation theory, we provide a criterion to identify the corresponding Tannaka super groups that applies in many situations. As an example we discuss the tensor category generated by the convolution powers of an algebraic curve inside its Jacobian variety.

Keywords

Tannakian category, tensor generator, symmetric square, alternating square, irreducible representation, reductive super group

Mathematical Subject Classification 2010

Primary: 20G05, 20C15

Secondary: 18D10

Milestones

Received: 5 March 2014

Revised: 6 November 2014

Accepted: 30 December 2014

Published: 1 July 2015