2014/09/04 by Michael Chmutov, Chmutov, Michael, Rachel Karpman +3
Mathematics · #Algebraic structures and combinatorial models #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory
paper · pdf · doi:10.48550/arxiv.1409.1305
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.