arXiv subjects
Publications and source records attributed to Aaron Wood.
Over a p-adic field of odd residual characteristic, Gan and Savin proved a correspondence between the Bernstein components of the even and odd Weil representations of the metaplectic group and the components of the trivial representation of the equal rank odd orthogonal groups. In this paper, we extend their result to the case of even residual characteristic.
For maximal compact subgroups of the metaplectic group, the minimal types in the Schrödinger model of the Weil representation are calculated explicitly. Although these types are known in the case of odd residual characteristic, this computation is done for arbitrary residual characteristic.
The Weil representation is used to construct a minimal type of the two-fold central extension of $\operatorname{Sp}_{2n}(\mathbb{Q}_2)$. The corresponding Hecke algebra is shown to be isomorphic to the classical affine Hecke algebra of the split adjoint orthogonal group $\operatorname{SO}_{2n+1}(\mathbb{Q}_2)$.