A superdimension formula for gl(m|n) modules
Representation Theory
2015-03-06 v2 Mathematical Physics
Combinatorics
math.MP
Abstract
We give a formula for the superdimension of a finite-dimensional simple gl(m|n)-module using the Su-Zhang character formula. As a corollary, we obtain a simple algebraic proof of a conjecture of Kac-Wakimoto for gl(m|n), namely, a simple module has nonzero superdimension if and only if it has maximal degree of atypicality. This conjecture was proven originally by Serganova using the Duflo-Serganova associated variety.
Cite
@article{arxiv.1409.1305,
title = {A superdimension formula for gl(m|n) modules},
author = {Michael Chmutov and Rachel Karpman and Shifra Reif},
journal= {arXiv preprint arXiv:1409.1305},
year = {2015}
}
Comments
7 pages, no figures