K-types and Invariants for the Representations of GSp(4,R)

Abstract

Automorphic representations of the adelic group GSp (4 ,A Q ) are of importance in their relation to Siegel modular forms of degree 2. Given an automorphic representation π of GSp (4 ,A Q ), it decomposes into a product of admissible representations at each place. In the non-archimedean case, many useful results have been produced by Roberts and Schmidt. Here we find some invariants for the case of GSp (4 ,R ), including the K -type structure, the L- and epsilon -factors, and the Gelfand-Kirillov dimension for all irreducible admissible representations.