The dependence on parameters of the inverse functor to the $K$-finite functor

Autor:	Wallach, Nolan R.
Rok vydání:	2020
Předmět:	Mathematics - Representation Theory
Druh dokumentu:	Working Paper
Popis:	An interpretation of the Casselman-Wallach (C-W) Theorem is that the $K$-finite functor is an isomorphism of categories from the category of finitely generated, admissible smooth Fr\'echet modules of moderate growth to the category of Harish-Chandra modules for a real reductive group, $G$ (here $K$ is a maximal compact subgroup of G).In this paper we study the dependence of this functor on parameters. Our main result implies that holomorphic dependence implies holomorphic dependence. The work uses results from the excellent thesis of van der Noort. Also a remarkable family of Universal Harish-Chandra modules developed in this paper plays a key role. Comment: arXiv admin note: substantial text overlap with arXiv:1902.01871
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2004.08391 Zobrazit plný text záznamu View this record from Arxiv