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Algebraic aspects of branching laws for holomorphic discrete series representations (Various Issues relating to Representation Theory and Non-commutative Harmonic Analysis)

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Bibliographic Information

Other Title
  • Algebraic aspects of branching laws for holomorphic discrete series representations

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Abstract

We consider the branching problem of holomorphic discrete series representations and their analytic continuation with respect to a symmetric subgroup of anti-holomorphic type. The main purpose is to prove the irreducibility of a (mathrm{g}oplus mathfrak{g}', $Delta$(G'))-module Homc(V, V')_{$Delta$(G')} for the underlying Harish-Chandra module V of a holomorphic discrete series representation and a generic (mathrm{g}', K')-module V'. Comparing the branching law of unitary representations to this result, we conjecture that the irreducibility of the (mathfrak{g}oplus mathfrak{g}', $Delta$(G'))-module Homc(V, V')_{triangle(G')} is related to the existence of a discrete spectrum.

Journal

  • RIMS Kokyuroku

    RIMS Kokyuroku 2031 180-190, 2017-05

    京都大学数理解析研究所

Details

  • CRID
    1050564288162753792
  • NII Article ID
    120006578978
  • NII Book ID
    AN00061013
  • ISSN
    18802818
  • HANDLE
    2433/236749
  • NDL BIB ID
    028508735
  • Text Lang
    ja
  • Article Type
    departmental bulletin paper
  • Data Source
    • IRDB
    • NDL
    • CiNii Articles

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