Tsukuba Journal of Mathematics

Representations of the normalizers of maximal tori of simple Lie groups

Jun-ichi Matsuzawa and Makoto Takahashi

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Abstract

We study the branching rule for the restriction from a complex simple Lie group $G$ to the normalizer of a maximal torus of $G$. We show that the problem is reduced to the determination of the Weyl group module structures induced on the zero weight spaces of representations of semisimple Lie groups. The concrete formulas are obtained for $SL$($n$, C) in terms of generalized q-binomial coeffcients and Schur functions.

Article information

Source
Tsukuba J. Math., Volume 33, Number 2 (2009), 189-237.

Dates
First available in Project Euclid: 26 February 2010

Permanent link to this document
https://projecteuclid.org/euclid.tkbjm/1267209418

Digital Object Identifier
doi:10.21099/tkbjm/1267209418

Mathematical Reviews number (MathSciNet)
MR2605853

Zentralblatt MATH identifier
1196.22010

Subjects
Primary: 22E46: Semisimple Lie groups and their representations 20C15: Ordinary representations and characters

Keywords
simple Lie groups normalizer of maximal torus representation branching rule

Citation

Matsuzawa, Jun-ichi; Takahashi, Makoto. Representations of the normalizers of maximal tori of simple Lie groups. Tsukuba J. Math. 33 (2009), no. 2, 189--237. doi:10.21099/tkbjm/1267209418. https://projecteuclid.org/euclid.tkbjm/1267209418


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