Schwartz homologies of representations of almost linear Nash groups

Let G be an almost linear Nash group, namely, a Nash group that admits a Nash homomorphism with finite kernel to some GLk(R). A homology theory (the Schwartz homology) is established for the category of smooth Fréchet representations of G of moderate growth. Frobenius reciprocity and Shapiro's...

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Bibliographic Details
Published inJournal of functional analysis Vol. 280; no. 7; p. 108817
Main Authors Chen, Yangyang, Sun, Binyong
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.04.2021
Subjects
Lie algebra homology
Schwartz homology
Schwartz induction
Tempered vector bundle
Tempered vector bundle
46T30
22E20
Schwartz induction
Schwartz homology
Lie algebra homology
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Summary:Let G be an almost linear Nash group, namely, a Nash group that admits a Nash homomorphism with finite kernel to some GLk(R). A homology theory (the Schwartz homology) is established for the category of smooth Fréchet representations of G of moderate growth. Frobenius reciprocity and Shapiro's lemma are proved in this category. As an application, we give a criterion for automatic extensions of Schwartz homologies of Schwartz sections of a tempered G-vector bundle.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2020.108817