Contractions of representations and algebraic families of harish-chandra modules
Joseph Bernstein, Nigel Higson, Eyal Subag
Institute for Gravitation & the Cosmos
Center for Fundamental Theory
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.
International Mathematics Research Notices
https://doi.org/10.1093/IMRN/RNY146
Mathematics(all)
10.1093/IMRN/RNY146
Dive into the research topics of 'Contractions of representations and algebraic families of harish-chandra modules'. Together they form a unique fingerprint.
Harish-Chandra Modules Mathematics 100%
Contraction Mathematics 57%
Family Mathematics 32%
Unitary Representation Mathematics 24%
Group Representation Mathematics 13%
Reductive Group Mathematics 12%
Unitary group Mathematics 12%
Filtration Mathematics 11%
Bernstein, J., Higson, N., & Subag, E. (2020). Contractions of representations and algebraic families of harish-chandra modules. International Mathematics Research Notices, 2020(11), 3494-3520. https://doi.org/10.1093/IMRN/RNY146
Bernstein, Joseph ; Higson, Nigel ; Subag, Eyal. / Contractions of representations and algebraic families of harish-chandra modules. In: International Mathematics Research Notices. 2020 ; Vol. 2020, No. 11. pp. 3494-3520.
@article{ca4eb59560e44d509f6b3b5cae280ec9,
title = "Contractions of representations and algebraic families of harish-chandra modules",
abstract = "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. ",
author = "Joseph Bernstein and Nigel Higson and Eyal Subag",
note = "Publisher Copyright: {\textcopyright} The Author(s) 2018.",
doi = "10.1093/IMRN/RNY146",
journal = "International Mathematics Research Notices",
Bernstein, J, Higson, N & Subag, E 2020, 'Contractions of representations and algebraic families of harish-chandra modules', International Mathematics Research Notices, vol. 2020, no. 11, pp. 3494-3520. https://doi.org/10.1093/IMRN/RNY146
Contractions of representations and algebraic families of harish-chandra modules. / Bernstein, Joseph; Higson, Nigel; Subag, Eyal.
In: International Mathematics Research Notices, Vol. 2020, No. 11, 2020, p. 3494-3520.
T1 - Contractions of representations and algebraic families of harish-chandra modules
AU - Bernstein, Joseph
AU - Higson, Nigel
AU - Subag, Eyal
N1 - Publisher Copyright: © The Author(s) 2018.
N2 - 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.
AB - 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.
U2 - 10.1093/IMRN/RNY146
DO - 10.1093/IMRN/RNY146
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
Bernstein J, Higson N, Subag E. Contractions of representations and algebraic families of harish-chandra modules. International Mathematics Research Notices. 2020;2020(11):3494-3520. doi: 10.1093/IMRN/RNY146