The Infinitesimal Characters of Discrete Series for Real Spherical Spaces

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Standard

The Infinitesimal Characters of Discrete Series for Real Spherical Spaces. / Krötz, Bernhard; Kuit, Job J.; Opdam, Eric M.; Schlichtkrull, Henrik.

In: Geometric and Functional Analysis, Vol. 30, No. 3, 2020, p. 804-857.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Krötz, B, Kuit, JJ, Opdam, EM & Schlichtkrull, H 2020, 'The Infinitesimal Characters of Discrete Series for Real Spherical Spaces', Geometric and Functional Analysis, vol. 30, no. 3, pp. 804-857. https://doi.org/10.1007/s00039-020-00540-6

APA

Krötz, B., Kuit, J. J., Opdam, E. M., & Schlichtkrull, H. (2020). The Infinitesimal Characters of Discrete Series for Real Spherical Spaces. Geometric and Functional Analysis, 30(3), 804-857. https://doi.org/10.1007/s00039-020-00540-6

Vancouver

Krötz B, Kuit JJ, Opdam EM, Schlichtkrull H. The Infinitesimal Characters of Discrete Series for Real Spherical Spaces. Geometric and Functional Analysis. 2020;30(3):804-857. https://doi.org/10.1007/s00039-020-00540-6

Author

Krötz, Bernhard ; Kuit, Job J. ; Opdam, Eric M. ; Schlichtkrull, Henrik. / The Infinitesimal Characters of Discrete Series for Real Spherical Spaces. In: Geometric and Functional Analysis. 2020 ; Vol. 30, No. 3. pp. 804-857.

Bibtex

@article{9f2acfa174904c2b9681db267486c5f1,
title = "The Infinitesimal Characters of Discrete Series for Real Spherical Spaces",
abstract = "Let Z= G/ H be the homogeneous space of a real reductive group and a unimodular real spherical subgroup, and consider the regular representation of G on L2(Z). It is shown that all representations of the discrete series, that is, the irreducible subrepresentations of L2(Z) , have infinitesimal characters which are real and belong to a lattice. Moreover, let K be a maximal compact subgroup of G. Then each irreducible representation of K occurs in a finite set of such discrete series representations only. Similar results are obtained for the twisted discrete series, that is, the discrete components of the space of square integrable sections of a line bundle, given by a unitary character on an abelian extension of H.",
author = "Bernhard Kr{\"o}tz and Kuit, {Job J.} and Opdam, {Eric M.} and Henrik Schlichtkrull",
year = "2020",
doi = "10.1007/s00039-020-00540-6",
language = "English",
volume = "30",
pages = "804--857",
journal = "Geometric and Functional Analysis",
issn = "1016-443X",
publisher = "Springer Basel AG",
number = "3",

}

RIS

TY - JOUR

T1 - The Infinitesimal Characters of Discrete Series for Real Spherical Spaces

AU - Krötz, Bernhard

AU - Kuit, Job J.

AU - Opdam, Eric M.

AU - Schlichtkrull, Henrik

PY - 2020

Y1 - 2020

N2 - Let Z= G/ H be the homogeneous space of a real reductive group and a unimodular real spherical subgroup, and consider the regular representation of G on L2(Z). It is shown that all representations of the discrete series, that is, the irreducible subrepresentations of L2(Z) , have infinitesimal characters which are real and belong to a lattice. Moreover, let K be a maximal compact subgroup of G. Then each irreducible representation of K occurs in a finite set of such discrete series representations only. Similar results are obtained for the twisted discrete series, that is, the discrete components of the space of square integrable sections of a line bundle, given by a unitary character on an abelian extension of H.

AB - Let Z= G/ H be the homogeneous space of a real reductive group and a unimodular real spherical subgroup, and consider the regular representation of G on L2(Z). It is shown that all representations of the discrete series, that is, the irreducible subrepresentations of L2(Z) , have infinitesimal characters which are real and belong to a lattice. Moreover, let K be a maximal compact subgroup of G. Then each irreducible representation of K occurs in a finite set of such discrete series representations only. Similar results are obtained for the twisted discrete series, that is, the discrete components of the space of square integrable sections of a line bundle, given by a unitary character on an abelian extension of H.

U2 - 10.1007/s00039-020-00540-6

DO - 10.1007/s00039-020-00540-6

M3 - Journal article

AN - SCOPUS:85088926597

VL - 30

SP - 804

EP - 857

JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

SN - 1016-443X

IS - 3

ER -

ID: 257709326