Restriction of Holomorphic Discrete Series to Real Forms
نویسنده
چکیده
Let G be a connected linear semisimple Lie group having a Holomorphic Discrete Series representation π. Let H be a connected reductive subgroupof G so that the global symmetric space attached to H is a real form of the Hermitian symmetric space associated to G. Fix a maximal compact subgroup K of G so that H ∩ K is a maximal compact subgroup for H. Let τ be the lowest K−type for π and let τ? denote the restriction of τ to H ∩ K . In this note we prove that the restriction of π to H is unitarily equivalent to the unitary representation of H induced by τ?.
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