The Infinitesimal Characters of Discrete Series for Real Spherical Spaces
Research output: Contribution to journal › Journal article › Research › peer-review
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
APA
Vancouver
Author
Bibtex
}
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