Contractions of representations and algebraic families of harish-chandra modules

Joseph Bernstein, Nigel Higson, Eyal Subag

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4 Scopus citations


We examine from an algebraic point of view some families of unitary group representations that arise in mathematical physics and are associated to contraction families of Lie groups. The contraction families of groups relate different real forms of a reductive group and are continuously parametrized, but the unitary representations are defined over a parameter subspace that includes both discrete and continuous parts. Both finite- and infinite-dimensional representations can occur, even within the same family. We shall study the simplest nontrivial examples and use the concepts of algebraic families of Harish-Chandra pairs and Harish-Chandra modules, introduced in a previous paper, together with the Jantzen filtration, to construct these families of unitary representations algebraically.

Original languageEnglish
Pages (from-to)3494-3520
Number of pages27
JournalInternational Mathematics Research Notices
Issue number11
StatePublished - 2020
Externally publishedYes

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