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Title: Poincaré series of holomorphic representations
Authors: Tan, E.-C. 
Zhu, C.-B. 
Issue Date: 25-Mar-1996
Citation: Tan, E.-C.,Zhu, C.-B. (1996-03-25). Poincaré series of holomorphic representations. Indagationes Mathematicae 7 (1) : 111-126. ScholarBank@NUS Repository.
Abstract: If V is a holomorphic representation of a Hermitian symmetric group G, we can define the Poincaré series of V by PV(t) = ∑λ (dimℂ Vλ)tλ where Vλ are the eigenspaces under the center of K, a maximal compact subgroup of G. We discuss properties of these formal power series, give explicit rational forms for some of the unitary holomorphic representations, and compute their Gelfand-Kirillov dimensions and Bernstein degrees (in the sense defined by Vogan).
Source Title: Indagationes Mathematicae
ISSN: 00193577
Appears in Collections:Staff Publications

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