Journal of Lie Theory 25 (2015), No. 4, 949--983
Copyright Heldermann Verlag 2015
Discrete Branching Laws for Minimal Holomorphic Representations
Dept. of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, OH 43210, U.S.A.
Kavli IPMU (WPI), The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa 277-8583, Japan
We find the explicit branching laws for the restriction of minimal holomorphic representations to symmetric subgroups in the case where the restriction is discretely decomposable. For holomorphic pairs the minimal holomorphic representation decomposes into a direct sum of lowest weight representations which is made explicit. For non-holomorphic pairs the restriction is shown to be irreducible and identified with a known representation. We further study a conjecture by Kobayashi on the behaviour of associated varieties under restriction and confirm this conjecture in the setting of this paper.
Keywords: Minimal representation, highest weight representation, branching law, discretely decomposable, associated variety.
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