Related papers: Local newforms for the general linear groups over …

We announce various results concerning the structure of compactly generated simple locally compact groups. We introduce a local invariant, called the structure lattice, which consists of commensurability classes of compact subgroups with…

A new family of local-global conjectures in the representation theory of finite groups has recently been proposed by Moret\'o. We show that one of the strongest of these conjectures, the strong subnormalizer conjecture, holds for…

We prove a decomposition of definable groups in o-minimal structures generalizing the Jordan-Chevalley decomposition of linear algebraic groups. It follows that any definable linear group G is a semidirect product of its maximal normal…

The local non-tempered Gan-Gross-Prasad conjecture suggests that, for a pair of irreducible Arthur type representations of two successive general linear groups, they have a non-zero Rankin-Selberg period if and only if they are "relevant".…

Let $F$ be a non archimedean local field of characteristic zero, we give a classification of generic representations of $GL(n,F)$ distinguished by a maximal Levi subgroup, in terms of inducing discrete series.

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 investigate the homogeneous $2$-local representations of the twin group $T_n$ for all integers $n\geqslant 2$. A complete classification is obtained, yielding three distinct families of representations. We show that each of these…

By the theory of Colmez and Fontaine, a de Rham representation of the Galois group of a local field roughly corresponds to a representation of the Weil-Deligne group equipped with an admissible filtration on the underlying vector space.…

In a previous article by the author and P. Wesolek, it was shown that a compactly generated locally compact group $G$ admits a finite normal series $(G_i)$ in which the factors are compact, discrete or irreducible in the sense that no…

We introduce invertible subalgebras of local operator algebras on lattices. An invertible subalgebra is defined to be one such that every local operator can be locally expressed by elements of the inveritible subalgebra and those of the…

In this note we classify the non-Noetherian generalized Heisenberg algebras H(f) introduced by Rencai L\"u and Kaiming Zhao [Linear Algebra Appl., 2015]. In case the polynomial f has degree greater than 1, we determine all locally finite…

In this paper, we classify conjugacy classes of centralizers of irreducible subgroups in $PSL(n,\mathbb{C})$ using alternate modules a.k.a. finite abelian groups with an alternate bilinear form. When $n$ is squarefree, we prove that these…

We give a general identity relating Eisenstein series on general linear groups. We do it by constructing an Eisenstein series, attached to a maximal parabolic subgroup and a pair of representations, one cuspidal and the other a character,…

Given a quaternionic form G of a p-adic classical group (p odd) we classify all cuspidal irreducible representations of G with coefficients in an algebraically closed field of characteristic different from p. We prove two theorems: At…

Let $F$ be a non-Archimedean locally compact field, let $G$ be a split connected reductive group over $F$. For a parabolic subgroup $Q\subset G$ and a ring $L$ we consider the $G$-representation on the $L$-module$$(*)\quad\quad\quad\quad…

We study the irreducible complex representations of general linear groups over principal ideal local rings of length two with a fixed finite residue field. We construct a canonical correspondence between the irreducible representations of…

Let F_0 be a non-archimedean local field of odd residual characteristic and let G be the unramified unitary group U(2,2) defined over F_0. In this paper, we give a classification of the irreducible smooth representations of G of…

We give an explicit recipe for determining iterated local cohomology groups with support in ideals of minors of a generic matrix in characteristic zero, expressing them as direct sums of indecomposable D-modules. For non-square matrices…

We give a classification for the irreducible $\mathfrak{u}$-diagonalizable representations of the degenerate affine Hecke algebra of type $G(\ell,1,n)$. Precisely we show that such $H_{\ell,n}$-modules are indexed by $\ell$-skew shapes and…

Lusztig has given a construction of certain representations of reductive groups over finite local principal ideal rings of characteristic p, extending the construction of Deligne and Lusztig of representations of reductive groups over…