A superdimension formula for (m | n)-modules

Michael Chmutov, Rachel Karpman, Shifra Reif

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We give a formula for the superdimension of a finite-dimensional simple (m|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 (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.

Original languageEnglish
Article number1650080
JournalJournal of Algebra and its Applications
Issue number5
StatePublished - 1 Jun 2016
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2016 World Scientific Publishing Company.


  • Lie superalgebra
  • character formula
  • superdimension formula


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