Journal of Lie Theory Ladder Representation Norms for Hermitian Symmetric Groups
نویسندگان
چکیده
Let G be a connected noncompact simple Hermitian symmetric group with nite center. Let H() denote the geometric realization of an irreducible unitary highest weight representation with highest weight. Then H() consists of vector-valued holomorphic functions on G=K and the action of G on H() is given in terms of a factor of automorphy. For highest weights corresponding to ladder representations, we obtain the G-invariant inner product on H(): This inner product arises as the pullback of an isom-etry : H()! H(~) Y ; where Y is nite dimensional and the weight ~ corresponds to a scalar valued representation. In all but nitely many cases the G-invariant inner product on H(~) is known and is used to express the G-invariant inner product on H(): Explicit examples are given for families of ladder representations of SU(p; q) and SO (2n). Finally, inversion formulas for unitary intertwining operators between H() and any equivalent realization are exhibited.
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