We generalize the methods of Moy-Prasad, in order to define and study the genuine depth zero representations of some nonlinear covers of reductive groups over p-adic local fields. In particular, we construct all depth zero supercuspidal representations of the metaplectic group Mp2n over a p-adic field of odd residue characteristic.

• Higher commutators • Godement’s principle: bounding dimensions of irreducibles • The von Neumann (strong) density theorem • Lie’s Theorem on irreducible finite-dimensional representations of connected solvable groups • Separating families of irreducible finite-dimensional representations • Subrepresentation Theorem for finite-dimensional representations of reductive linear real Lie groups • T...

We give a geometric proof of a “parity-switching” phenomenon that occurs when applying the local Langlands and Jacquet–Langlands correspondence to a self-dual supercuspidal representation ofGL(n) over a nonarchimedean local field. This turns out to reflect a duality property on the self-dual part of the `-adic étale cohomology of the Lubin–Tate tower.

We study components of the Bernstein decomposition of 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.

In this paper we give an explicit parameterization of the local theta correspondence of supercuspidal representations for the reductive dual pairs (U1(F ),U1(F )), (U1(F ),U1,1(F )), (U1(F ),U2(F )), and (U1(F ),U1,2(F )) of unitary groups over a nonarchimedean local field F of odd residue characteristic.

The purpose of this article was to assess the overall health behaviors of African American emerging adults who live in a Midwestern city. Two hundred participants, ages 18-25, completed a 129-item survey. Results indicate that African American emerging adults are engaged in relatively healthy behaviors (i.e., physical activity, low substance use). The results also showed that within the emergin...