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

2022/05/15 by Arashi, Koichi
#53C55 #FOS: Mathematics #Primary: 22E27 #Representation Theory (math.RT) #Secondary: 32M05

paper · doi:10.48550/arxiv.2205.07262

Abstract

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.

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