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arXiv · 2002.09378

Action of the restricted Weyl group on the $L$-invariant vectors of a representation

Ilia Smilga
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Abstract

This note constitutes a brief survey of our recent work on the problem of determining, for a given real Lie group~$G$, the set of representations~$V$ in which the longest element~$w_0$ of the restricted Weyl group~$W$ acts nontrivially on the subspace~$V^L$ of~$V$ formed by vectors that are invariant by~$L$, the centralizer of a maximal split torus of~$G$.

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Ilia Smilga. 2020-02-21. Action of the restricted Weyl group on the $L$-invariant vectors of a representation. https://doi.org/10.1007/978-981-15-7775-8_27

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