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

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

Keywords

Lie superalgebra
character formula
superdimension formula

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Applied Mathematics

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10.1142/S0219498816500808

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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.",

keywords = "Lie superalgebra, character formula, superdimension formula",

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T1 - A superdimension formula for (m | n)-modules

AU - Chmutov, Michael

AU - Karpman, Rachel

AU - Reif, Shifra

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N2 - 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.

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.

KW - Lie superalgebra

KW - character formula

KW - superdimension formula

UR - http://www.scopus.com/inward/record.url?scp=84962766383&partnerID=8YFLogxK

U2 - 10.1142/S0219498816500808

DO - 10.1142/S0219498816500808

M3 - مقالة

SN - 0219-4988

VL - 15

JO - Journal of Algebra and its Applications

JF - Journal of Algebra and its Applications

IS - 5

M1 - 1650080

ER -

A superdimension formula for (m | n)-modules

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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