An irreducible decomposition of the Weil representation restricted to open compact subgroups

Abstract

For a $p$-adic field of any residual characteristic, we determine irreducible decompositions of the Weil representation restricted to the maximal open compact subgroups and the Iwahori subgroup by using the Schrödinger model. In particular, these decompositions show that the restrictions are multiplicity free.

arXiv comment37 pages