Morita's Theory for the Symplectic Groups

Abstract

We construct and study the holomorphic discrete series representation and the principal series representation of the symplectic group $\mathrm{Sp}(2n,F)$ over a $p$-adic field $F$ as well as a duality between some sub-representations of these two representations. The constructions of these two representations generalize those defined in Morita and Murase's works. Moreover, Morita built a duality for $\mathrm{SL}(2,F)$ defined by residues. We view the duality we defined as an algebraic interpretation of Morita's duality in some extent and its generalization to the symplectic groups.

23 pages

Cited by in corpus (1)

• Morita's Duality for Split Reductive Groups