Related papers: A Simple Generalised Plancherel Formula for Compac…

We construct an analogue of Whittaker reduction for Poisson actions of a semisimple complex Poisson-Lie group G. The reduction takes place along a class of transversal slices to unipotent orbits in G, which are generalizations of the…

Lapid and Mao conjectured Ichino-Ikeda type formula of Whittaker periods for any quasi-split reductive groups and metaplectic groups. In this paper, we prove this formula for any irreducible cuspidal globally generic automorphic…

In this paper, we define compact open subgroups of quasi-split even unitary groups for each even non-negative integers, and establish the theory of local newforms for irreducible tempered generic representations with a certain condition on…

Let G be a semisimple group over an algebraically closed field of characteristic p>0. We give a (partly conjectural) simple, closed formula for the character of many indecomposable tilting rational G-modules, assuming that p is large.

We obtain two explicit formulas for the full local character expansion of any irreducible representation of a p-adic general linear group in principal blocks. The first, generalizing previous work of the author on the Iwahori-spherical…

It is well known that for irreducible, square-integrable representations of a locally compact group, there exist so-called admissible vectors which allow the construction of generalized continuous wavelet transforms. In this paper we…

We give a normalizer decomposition for a p-local compact group (S, F, L) that describes |L| as a homotopy colimit indexed over a finite poset. Our work generalizes the normalizer decompositions for finite groups due to Dwyer, for p-local…

We show a matrix Paley-Wiener theorem for the Hecke algebra of a p-adic group. The proof is based on an analogue of Harish-Chandra's Plancherel formula.

The Plancherel formula for the universal covering group of $SL(2, R)$ derived earlier by Pukanszky on which Herb and Wolf build their Plancherel theorem for general semisimple groups is reconsidered. It is shown that a set of unitarily…

Let S be a locally noetherian regular scheme. We compute the units-Picard complex of a reductive S-group scheme G in terms of the dual algebraic fundamental complex of G. To do so, we establish a units-Picard-Brauer exact sequence for a…

We define the ``lifted character'' of mod-$\ell$ representations of $p$-adic reductive groups where $\ell\not=p$, on compact elements with pro-orders not divisible by $\ell$. We generalize the local character expansion results of Howe,…

In this article, we present a concise combinatorial formula for efficiently determining the Wedderburn decomposition of rational group algebra associated with a split metacyclic $p$-group $G$, where $p$ is an odd prime. We also provide a…

We provide a Plancherel decomposition for the space of symplectic bilinear forms of rank $2n$ over a local non-archimedean field $F$ in terms of that of $GL_n(F)$.

In this note we reformulate the spectral side of the Weyl law in the language of the matrix-valued quantisation on compact Lie groups.

We consider the minimal representation of (a finite cover of) the conformal group of a simple split Jordan algebra over $\mathbb{R}$ or $\mathbb{C}$, whenever it exists. The conformal group contains a natural dual pair $G\times G'$, where…

We discuss various forms of the Plancherel Formula and the Plancherel Theorem on reductive groups over local fields.

Let $G$ be a unimodular locally compact group. We define a property of irreducible unitary $G$-representations $V$ which we call c-temperedness, and which for the trivial $V$ boils down to F{\o}lner's condition (equivalent to the trivial…

In this article, we present a combinatorial formula for computing the Wedderburn decomposition of the rational group algebra associated with an ordinary metacyclic $p$-group $G$, where $p$ is any prime. We also provide a formula for…

This paper is concerned with representations of split orthogonal and quasi-split unitary groups over a nonarchimedean local field which are not generic, but which support a unique model of a different kind, the generalized Bessel model. The…

Given a spherical variety X for a group G over a non-archimedean local field k, the Plancherel decomposition for L^2(X) should be related to "distinguished" Arthur parameters into a dual group closely related to that defined by Gaitsgory…