On the action of the $$U_p$$ operator on the local (at p) representation attached to congruence level Siegel modular forms.

In this article, we study the action of the $$U_p$$ Hecke operator on the normalized spherical vector $$\phi $$ in the representation of $${{\mathrm{GSp}}}_4(\mathbf {Q}_p)$$ induced from a character on the Borel subgroup. We compute the Petersson norm of $$U_p \phi $$ in terms of certain local L-values associated with $$\phi $$ . [ABSTRACT FROM AUTHOR]