Covers for Self-dual Supercuspidal Representations of the Siegel Levi Subgroup of Classical p-adic Groups

We study components of the Bernstein decomposition for a p-adic classical group (with p odd) with inertial support a self-dual positive level supercuspidal representation of a Siegel Levi subgroup. More precisely, we use the method of covers to construct a Bushnell-Kutzko type for such a component. A detailed knowledge of the Hecke algebra of the type should have number-theoretic implications.