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arXiv:1409.1305 [math.RT]AbstractReferencesReviewsResources

A superdimension formula for gl(m|n) modules

Michael Chmutov, Rachel Karpman, Shifra Reif

Published 2014-09-04Version 1

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.

Comments: 6 pages, no figures
Categories: math.RT, math-ph, math.CO, math.MP
Subjects: 17B10
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