Algebraic families of Harish-Chandra pairs

Joseph Bernstein; Nigel Higson; Eyal Subag

doi:10.1093/IMRN/RNY147

Algebraic families of Harish-Chandra pairs

Joseph Bernstein, Nigel Higson, Eyal Subag

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Abstract

Mathematical physicists have studied degenerations of Lie groups and their representations, which they call contractions. In this paper we study these contractions, and also other families, within the framework of algebraic families of Harish-Chandra modules. We construct a family that incorporates both a real reductive group and its compact form, separate parts of which have been studied individually as contractions. We give a complete classification of generically irreducible families of Harish-Chandra modules in the case of the family associated to SL(2, R).

Original language	English
Pages (from-to)	4776-4808
Number of pages	33
Journal	International Mathematics Research Notices
Volume	2020
Issue number	15
DOIs	https://doi.org/10.1093/IMRN/RNY147
State	Published - 2020
Externally published	Yes

Bibliographical note

Publisher Copyright:
© The Author(s) 2018.

Funding

This work was supported by the European Research Council [grant 291612 to J.B. and E.S.] and the US National Science Foundation [grant DMS-1101382 to N.H.].

Funders	Funder number
National Science Foundation	DMS-1101382
European Commission	291612

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10.1093/IMRN/RNY147

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Algebraic families of Harish-Chandra pairs

Abstract

Bibliographical note

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