A minimal even type of the 2-adic Weil representation

Abstract: The Weil representation is used to construct a minimal type of the two-fold central extension of $\operatorname{Sp}<em>{2n}(\mathbb{Q}_2)$. The corresponding Hecke algebra is shown to be isomorphic to the classical affine Hecke algebra of the split adjoint orthogonal group $\operatorname{SO}</em>{2n+1}(\mathbb{Q}_2)$.