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.
Publié le : 2009-12-15
Classification:
simple Lie groups,
normalizer of maximal torus,
representation,
branching rule,
22E46,
20C15
@article{1267209418,
author = {Matsuzawa, Jun-ichi and Takahashi, Makoto},
title = {Representations of the normalizers of maximal tori of simple Lie
groups},
journal = {Tsukuba J. Math.},
volume = {33},
number = {2},
year = {2009},
pages = { 189-237},
language = {en},
url = {http://dml.mathdoc.fr/item/1267209418}
}
Matsuzawa, Jun-ichi; Takahashi, Makoto. Representations of the normalizers of maximal tori of simple Lie
groups. Tsukuba J. Math., Tome 33 (2009) no. 2, pp. 189-237. http://gdmltest.u-ga.fr/item/1267209418/