Klingen p^2 vectors for GSp(4)

Shaoyun Yi – University of Oklahoma

In 2007, Roberts and Schmidt had a satisfactory local theory of new- and oldforms for GSp(4) with trivial central character, in which they considered the vectors fixed by the paramodular groups K(p^n). In this talk, we consider the vectors fixed by the Klingen subgroup of level p^2. We calculate the dimensions of the spaces of these invariant vectors for all irreducible, admissible representations of GSp(4, F), where F is a p-adic field.