Representations of division algebras over local fields

Refined anisotropic K-types and supercuspidal representations

“…9, we show that the Moy-Prasad filtrations and the mock exponential maps are compatible with restriction to such subgroups.…”

The Plancherel formula, the Plancherel theorem, and the Fourier transform of orbital integrals

“…It is difficult to associate certain characters with any particular torus, as well as to tell when representations constructed from different tori are distinct. We also mention the work of Corwin on division algebras in both the tame [14] and the wild [15] case.…”

Supercuspidal components of the quaternion Weil representation of SL2(k)

“…From Proposition 1.5 of [4], we may conclude that H\U)@H\U) and H θ \U)ζ&H θ "{U) are both G-invariant. (See also Lemma 4.1 of [3].) 5* From [5] and [7], we know that all supercuspidal representations of G are induced from some compact open subgroup.…”

“…The object of this paper is to show just how these representations correspond to summands of quadratic extension Weil representations. The methods depend heavily on [3]. The primary motivation for this paper was the problem of decomposing tensor products of certain supercuspidal representations of G. The authors have been told that some similar computations have been worked out by J.…”

“…From [3], we recall some information on the representations 36 C. ASMUTH AND J. REPKA of Γ-{γeD: v D {y) = 1}. Let C θ = {ze l(vT): v θ {z) = 1}.…”