Finite multiplicity theorems for induction and restriction

DOI10.1016/J.AIM.2013.07.015zbMATH Open1317.22010arXiv1108.3477OpenAlexW2064609849MaRDI QIDQ2437543

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Publication date: 3 March 2014

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Abstract: We find upper and lower bounds of the multiplicities of irreducible admissible representations $pi$ of a semisimple Lie group $G$ occurring in the induced representations $In{d}_H^{G}au$ from irreducible representations $au$ of a closed subgroup $H$. As corollaries, we establish geometric criteria for finiteness of the dimension of $Ho{m}_G(pi,In{d}_H^{G}au)$ (induction) and of $Ho{m}_H(pi{|}_H,au)$ (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.

Full work available at URL: https://arxiv.org/abs/1108.3477

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