The Infinitesimal Characters of Discrete Series for Real Spherical Spaces
The Infinitesimal Characters of Discrete Series for Real Spherical Spaces
复制标题
实球空间离散级数的无穷小特征
DOI：
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发表时间：
2017
影响因子：
2.2
通讯作者：
H. Schlichtkrull
中科院分区：
文献类型：
--
作者：
Bernhard Krötz;Job J. Kuit;E. Opdam;H. Schlichtkrull
Let Z=G/Hdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$Z=G/H$$end{document} 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)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$L^2(Z)$$end{document}. It is shown that all representations of the discrete series, that is, the irreducible subrepresentations of L2(Z)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$L^2(Z)$$end{document}, 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.
Let Z=G/Hdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$Z=G/H$$end{document} 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)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$L^2(Z)$$end{document}. It is shown that all representations of the discrete series, that is, the irreducible subrepresentations of L2(Z)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$L^2(Z)$$end{document}, 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.
还原李群表示的波前集 III
影响因子：
1.7
作者：
B. Harris;T. Weich
通讯作者：
T. Weich