A Generating Function for Blattner’s Formula
نویسنده
چکیده
Abstract. Let G be a connected, semisimple Lie group with finite center and let K be a maximal compact subgroup. We investigate a method to compute multiplicities of K-types in the discrete series using a rational expression for a generating function obtained from Blattner’s formula. This expression involves a product with a character of an irreducible finite dimensional representation of K and is valid for any discrete series system. We consider the situation for split G2 in detail. Other results include a new proof of a symmetry of Blattner’s formula. The motivation for this paper came from an attempt to understand pictures coming from Blattner’s formula, some of which we include in the last section.
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