Journal of Lie Theory 12 (2002), No. 2, 409--421
Copyright Heldermann Verlag 2002
Vanishing Properties of Analytically Continued Matrix Coefficients
Bernhard Krötz
Dept. of Mathematics, Ohio State University, 231 West 18th Avenue, Columbus, OH 43210-1174, U.S.A.
Michael Otto
Dept. of Mathematics, Ohio State University, 231 West 18th Avenue, Columbus, OH 43210-1174, U.S.A.
We consider (generalized) matrix coefficients associated to irreducible unitary representations of a simple Lie group G which admit holomorphic continuation to a complex semigroup domain S, subset of GC. Vanishing theorems for these analytically continued matrix coefficients, one of Howe-Moore type and one for cusp forms, are proved.
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