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arXiv · 1108.3477

Finite multiplicity theorems for induction and restriction

Toshiyuki Kobayashi·Toshio Oshima
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Abstract

We find upper and lower bounds of the multiplicities of irreducible admissible representations $π$ of a semisimple Lie group $G$ occurring in the induced representations $Ind_H^Gτ$ from irreducible representations $τ$ of a closed subgroup $H$. As corollaries, we establish geometric criteria for finiteness of the dimension of $Hom_G(π,Ind_H^G τ)$ (induction) and of $Hom_H(π|_H,τ)$ (restriction) by means of the real flag variety $G/P$, and discover that uniform boundedness property of these multiplicities is independent of real forms and characterized by means of the complex flag variety.

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BibTeXRIS

Toshiyuki Kobayashi, Toshio Oshima. 2013-08-01. Finite multiplicity theorems for induction and restriction. https://doi.org/10.1016/j.aim.2013.07.015

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