科研之友
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摘要
We give a formula for the superdimension of a finite-dimensional simple gl(m vertical bar n)-module using the Su-Zhang character formula. This formula coincides with the superdimension formulas proven by Weissauer and Heidersdorf-Weissauer. As a corollary, we obtain a simple algebraic proof of a conjecture of Kac-Wakimoto for gl(m vertical bar 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.
- 出版日期2016-6
