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arXiv · 1409.1305

A superdimension formula for gl(m|n) modules

Michael Chmutov·Rachel Karpman·Shifra Reif
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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.

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BibTeXRIS

Michael Chmutov, Rachel Karpman, Shifra Reif. 2014-09-04. A superdimension formula for gl(m|n) modules. https://arxiv.org/abs/1409.1305

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