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We give a motivic proof of a character formula for depth zero supercuspidal representations of $p$-adic SL(2). We begin by finding the virtual Chow motives for the character values of all depth zero supercuspidal representations of $p$-adic SL(2), at topologically unipotent elements. Then we find the virtual Chow motives for the values of the Fourier transform of all regular elliptic orbital integrals with depth zero in their Cartan subalgebra, at topologically nilpotent elements. Finally, we prove a character formula for depth zero supercuspidal representations by showing that the formula corresponds to three identities in the ring of virtual Chow motives over $mathbb{Q}$.
In this note, we establish a version of the local Cauchy-Crofton formula for definable sets in Henselian discretely valued fields of characteristic zero. It allows to compute the motivic local density of a set from the densities of its projections integrated over the Grassmannian.
We generalize a result by Cunningham-Salmasian to a Mackey-type formula for the compact restriction of a semisimple perverse sheaf produced by parabolic induction from a character sheaf, under certain conditions on the parahoric group used to define
In this note, we give a short proof of the localization formula for the loop space Chern character of a compact Riemannian spin manifold M, using the rescaled spinor bundle on the tangent groupoid associated to M.
Let B be a reductive Lie subalgebra of a semi-simple Lie algebra of the same rank both over the complex numbers. To each finite dimensional irreducible representation $V_lambda$ of F we assign a multiplet of irreducible representations of B with m el
We compute the Hodge-Deligne polynomials of the moduli spaces of representations of the fundamental group of a complex surface into SL(2,C), for the case of small genus g, and allowing the holonomy around a fixed point to be any matrix of SL(2,C), th