Standard tableaux and Klyachko's theorem on Lie representations

Marianne Johnson

doi:10.1016/j.jcta.2006.02.002

Standard tableaux and Klyachko's theorem on Lie representations

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

Abstract

We show that for all but two partitions λ of n > 6 there exists a standard tableau of shape λ with major index coprime to n. In conjunction with a deep result of Kraśkiewicz and Weyman this provides a new purely combinatorial proof of Klyachko's famous theorem on Lie representations of the general linear group. © 2006 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	151-158
Number of pages	7
Journal	Journal of Combinatorial Theory. Series A
Volume	114
Issue number	1
DOIs	https://doi.org/10.1016/j.jcta.2006.02.002
Publication status	Published - Jan 2007

Keywords

Free Lie algebra
Lie representation
Standard tableau

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10.1016/j.jcta.2006.02.002

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title = "Standard tableaux and Klyachko's theorem on Lie representations",

abstract = "We show that for all but two partitions λ of n > 6 there exists a standard tableau of shape λ with major index coprime to n. In conjunction with a deep result of Kra{\'s}kiewicz and Weyman this provides a new purely combinatorial proof of Klyachko's famous theorem on Lie representations of the general linear group. {\textcopyright} 2006 Elsevier Inc. All rights reserved.",

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author = "Marianne Johnson",

year = "2007",

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doi = "10.1016/j.jcta.2006.02.002",

language = "English",

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AB - We show that for all but two partitions λ of n > 6 there exists a standard tableau of shape λ with major index coprime to n. In conjunction with a deep result of Kraśkiewicz and Weyman this provides a new purely combinatorial proof of Klyachko's famous theorem on Lie representations of the general linear group. © 2006 Elsevier Inc. All rights reserved.

KW - Free Lie algebra

KW - Lie representation

KW - Standard tableau

U2 - 10.1016/j.jcta.2006.02.002

DO - 10.1016/j.jcta.2006.02.002

M3 - Article

SN - 1096-0899

VL - 114

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JO - Journal of Combinatorial Theory. Series A

JF - Journal of Combinatorial Theory. Series A

IS - 1

ER -

Standard tableaux and Klyachko's theorem on Lie representations

Abstract

Keywords

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