Related papers: Some unipotent Arthur packets for p-adic split F4

We classify the irreducible unitary modules in category O for the rational Cherednik algebras of type G(r,1,n) and give explicit combinatorial formulas for their graded characters. More precisely, we produce a combinatorial algorithm…

We extend the Larson-Sweedler theorem to weak Hopf algebras by proving that a finite dimensional weak bialgebra is a weak Hopf algebra iff it possesses a non-degenerate left integral. We show that the category of modules over a weak Hopf…

A new class of locally unital and locally finite dimensional algebras $A$ over an arbitrary algebraically closed field is discovered. Each of them admits an upper finite weakly triangular decomposition, a generalization of an upper finite…

We prove that the space $\mathscr{P}(\mathfrak{A})$ of pure states of a nonelementary, simple, separable, real rank zero $C^*$-algebra $\mathfrak{A}$ has trivial homotopy groups of all orders when $\mathscr{P}(\mathfrak{A})$ is equipped…

We provide a construction of local and automorphic non-tempered Arthur packets of the group SO(3,2) and its inner form SO(4,1) associated with a certain Arthur's parameter and prove a multiplicity formula. We further study the restriction…

In this paper we present a construction of the compact form of the exceptional Lie group F4 by exponentiating the corresponding Lie algebra f4. We realize F4 as the automorphisms group of the exceptional Jordan algebra, whose elements are 3…

We construct all cuspidal l-modular representations of a unitary group in three variables attached to an unramified extension of local fields of odd residual characteristic p with l\neq p. We describe the l-modular principal series and show…

We show that the definition of unipotent (resp. nilpotent) pieces for classical groups given by Lusztig (resp. Lusztig and the author) coincides with the combinatorial definition using closure relations on unipotent classes (resp. nilpotent…

We construct local Arthur packets associated with a dihedral long root $A$-parameter of a split reductive group of type $G_2$ over a nonarchimedian local field of characteristic zero. The construction relies on an exceptional correspondence…

Weak topological phases are usually described in terms of protection by the lattice translation symmetry. Their characterization explicitly relies on periodicity since weak invariants are expressed in terms of the momentum-space torus. We…

Let $G_n$ denote either the group $Sp(2n, F)$ or $SO(2n+1, F)$ over a non-archimedean local field $F$. We determine the composition series of representations of $G_n$ induced from cuspidal and ladder representations such that the minimal…

Let $Z=G/H$ be the homogeneous space of a real reductive group and a unimodular real spherical subgroup, and consider the regular representation of $G$ on $L^2(Z)$. It is shown that all representations of the discrete series, that is, the…

We prove a conjecture of the first-named author ([J14]) on the upper bound Fourier coefficients of automorphic forms in Arthur packets of all classical groups over any number field. This conjecture generalizes the global version of the…

Let $G$ be a simple algebraic group defined over a finite field of good characteristic, with associated Frobenius endomorphism $F$. In this article we extend an observation of Lusztig, (which gives a numerical relationship between an…

We study a new lifting of automorphic representations using the theta representation $\Theta$ on the $4$-fold cover of the symplectic group, $\overline{\mathrm{Sp}}_{2r}(\mathbb{A})$. This lifting produces the first examples of CAP…

Let H be a Hecke algebra arising as an endomorphism algebra of the representation of a Chevalley group G over F_q induced by a unipotent cuspidal representation of a Levi quotient L of a parabolic subgroup. We assume that L is not a torus.…

Using the notion of a Lagrangian covering, W. Graham and D. Vogan proposed a method of constructing representations from the coadjoint orbits for a complex semisimple Lie group $G$. When the coadjoint orbit $\calO$ is nilpotent, a…

Let $\mathrm G / F$ be a reductive split $p$-adic group and let $\mathrm U$ be the unipotent radical of a Borel subgroup. We study the cohomology with trivial $\mathbb Z_p$-coefficients of the profinite nilpotent group $N = \mathrm…

With a view to determining character values of finite reductive groups at unipotent elements, we prove a number of results concerning inner products of generalised Gelfand-Graev characters with characteristic functions of character sheaves,…

Let F_0 be a non-archimedean local field of odd residual characteristic and let G be the non quasi-split unramified unitary group in four variables defined over F_0. In this paper, we give a classification of the irreducible smooth…