## Tsukuba Journal of Mathematics

### Representations of the normalizers of maximal tori of simple Lie groups

#### 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

https://projecteuclid.org/euclid.tkbjm/1267209418

Digital Object Identifier
doi:10.21099/tkbjm/1267209418

Mathematical Reviews number (MathSciNet)
MR2605853

Zentralblatt MATH identifier
1196.22010

#### 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