A superdimension formula for (m | n)-modules

Michael Chmutov; Rachel Karpman; Shifra Reif

doi:10.1142/S0219498816500808

A superdimension formula for (m | n)-modules

Michael Chmutov, Rachel Karpman, Shifra Reif

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

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 language	English
Article number	1650080
Journal	Journal of Algebra and its Applications
Volume	15
Issue number	5
DOIs	https://doi.org/10.1142/S0219498816500808
State	Published - 1 Jun 2016
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2016 World Scientific Publishing Company.

Keywords

Lie superalgebra
character formula
superdimension formula

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10.1142/S0219498816500808

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AB - 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.

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KW - character formula

KW - superdimension formula

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A superdimension formula for (m | n)-modules

Abstract

Bibliographical note

Keywords

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