Abstract In this paper we prove Vogan’s conjecture on local Arthur packets, as recalled in Cunningham et al. [Arthur packets for p-adic groups by way of microlocal vanishing cycles perverse sheaves, with examples, Memoirs the American Mathematical Society, Boston, 2022, Section 8.3, Conjecture 1(a)], irreducible parameters p -adic general linear groups. This result shows that these may be chara...

In this paper we study reducibility of those representations of quasi-split unitary p-adic groups which are parabolically induced from supercuspidal representations of general linear groups. For a supercuspidal representation associated via Howe’s construction to an admissible character, we show that in many cases a criterion of Goldberg for reducibility of the induced representation reduces to...

In this paper, we study Jacquet modules for p-adic general linear groups. More precisely, we have results—formulas and algorithms—aimed at addressing the following question: Given the Langlands data for an irreducible representation, can we determine its (semisimplified) Jacquet module? We use our results to answer this question in a number of cases, as well as to recover some familiar results ...

We show that, under fairly general conditions, many elements of a p-adic group can be well approximated by a product whose factors have properties that are helpful in performing explicit character computations.

This paper is a continuation of [3] in which the first two authors have introduced the spherical Hecke algebra and the Satake isomorphism for an untwisted affine Kac-Moody group over a non-archimedian local field. In this paper we develop the theory of the Iwahori-Hecke algebra associated to these same groups. The resulting algebra is shown to be closely related to Cherednik’s double affine Hec...

Given an integer n and a group G we estimate the probability that a random, monic, degree n, p-adic polynomial has Galois group isomorphic to G. A comparison is made with classic results concerning Galois groups of random, monic, degree n polynomials with integer coefficients. We conclude by analyzing the probability that a random, monic, degree n polynomial in Z[x] has these properties: its Ga...

For a certain class of locally profinite groups, we show that an irreducible smooth discrete series representation is necessarily supercuspidal and, more strongly, can be obtained by induction from a linear character of a suitable open and compact modulo center subgroup. If F is a non-Archimedean local field, then our class of groups includes the groups of F -points of unipotent algebraic group...

The orbit method conjectures a close relationship between the set of irreducible unitary representations of a Lie group G, and admissible coadjoint orbits in the dual of the Lie algebra. We define admissibility for nilpotent coadjoint orbits of p-adic reductive Lie groups, and compute the set of admissible orbits for a range of examples. We find that for unitary, symplectic, orthogonal, general...

We introduced the continuous and discrete $p$-adic shearlet systems. We restrict ourselves to a brief description of the $p$-adic theory and shearlets in real case. Using the group $G_p$ consist of all $p$-adic numbers that all of its elements have a square root, we defined the continuous $p$-adic shearlet system associated with $L^2left(Q_p^{2}right)$. The discrete $p$-adic shearlet frames for...