arXiv subjects

Koichi Arashi

Publications and source records attributed to Koichi Arashi.

3 recordsLinked to original sources

arXiv2025

Multiplicity-free representations and coisotropic actions of certain nilpotent Lie groups over quasi-symmetric Siegel domains

We study multiplicity-free representations of Lie groups over a quasi-symmetric Siegel domain, with a focus on certain two-step nilpotent Lie groups. We provide necessary and sufficient conditions for the multiplicity-freeness property to hold. Specifically, we establish the equivalence between the disjointness of irreducible unitary representations realized over the domain, the multiplicity-freeness of the unitary representation on the Bergman space, and the coisotropicity of the group action.

math.RT↗

arXiv2024

Multiplicity-free representations of certain nilpotent Lie groups over Siegel domains of the second kind

We investigate the multiplicity-freeness property for the holomorphic multiplier representations of affine transformation groups of a Siegel domain of the second kind. We deal with the generalized Heisenberg group and its subgroups. Necessary and sufficient conditions for a specific representation to be multiplicity-free are provided. We study the multiplicity-freeness property in relation to the geometrical notions of coisotropic action and visible action, and also the commutativity of the algebra of invariant differential operators.

math.RT↗

arXiv2023

Coherent state representations of the holomorphic automorphism group of a quasi-symmetric Siegel domain of type III

The aim of this paper is to study the classification of generic coherent state representations of a Lie group and its connection to the structure theory of Kähler algebras. The group we deal with is the holomorphic automorphism group of a quasi-symmetric Siegel domain of type III. A method using the generalized Iwasawa decomposition is provided.

math.RT↗