Proceedings of the Japan Academy, Series A, Mathematical Sciences

Admissible representations, multiplicity-free representations and visible actions on non-tube type Hermitian symmetric spaces

Atsumu Sasaki

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Abstract

This paper presents new characterization for a non-compact Hermitian symmetric space $G/K$ to be of tube type (or non-tube type) by multiplicities in some branching laws and visible actions. The study in this paper gives an example of a kind of the Cartan decomposition for non-symmetric homogeneous spaces.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 91, Number 5 (2015), 70-75.

Dates
First available in Project Euclid: 30 April 2015

Permanent link to this document
https://projecteuclid.org/euclid.pja/1430397896

Digital Object Identifier
doi:10.3792/pjaa.91.70

Mathematical Reviews number (MathSciNet)
MR3342030

Zentralblatt MATH identifier
1333.22011

Subjects
Primary: 22E46: Semisimple Lie groups and their representations
Secondary: 32M15: Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras [See also 22E10, 22E40, 53C35, 57T15] 14M17: Homogeneous spaces and generalizations [See also 32M10, 53C30, 57T15]

Keywords
Multiplicity-free representation admissible representation visible action (real) spherical variety Hermitian symmetric space tube type domain

Citation

Sasaki, Atsumu. Admissible representations, multiplicity-free representations and visible actions on non-tube type Hermitian symmetric spaces. Proc. Japan Acad. Ser. A Math. Sci. 91 (2015), no. 5, 70--75. doi:10.3792/pjaa.91.70. https://projecteuclid.org/euclid.pja/1430397896


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