Related papers: Quaternionic symplectic model for discrete series …

Let G be a subgroup of GL(V), where V is a finite dimensional vector space over a finite field of characteristic p >0. If det(g-1) = 0 for all g \in G then we call G a fixed-point subgroup of GL(V). Motivated in parallel by questions in…

Let U(N) be the quasi-split unitary group in N variables for a quadratic unramified extension of p-adic fields. We compute the characters of simple supercuspidal representations of twisted GL(N) and U(N). Comparing them by the endoscopic…

We develop representation theory of general linear groups in the category $\text{Ver}_4^+$, the simplest tensor category which is not Frobenius exact. Since $\text{Ver}_4^+$ is a reduction of the category of supervector spaces to…

Let F be a non-archimedean local field of odd residual characteristic. Let G be a (connected) reductive group over F that splits over a tamely ramified field extension of F. We revisit Yu's construction of smooth complex representations of…

The formal degree of a unipotent discrete series character of a simple linear algebraic group over a non-archimedean local field (in the sense of Lusztig), is a rational function of the cardinality q of the residue field. The irreducible…

Let K be a non-archimedean local field and let G be a connected reductive K-group which splits over an unramified extension of K. We investigate supercuspidal unipotent representations of the group G(K). We establish a bijection between the…

We recast spinful superconductivity as a \textit{quaternion field theory}, where a quaternion is a four-component hypercomplex number with units $(\boldsymbol{e}_x,\boldsymbol{e}_y,\boldsymbol{e}_z)$, that encodes the spin-singlet/triplet…

This paper provides a complete classification of $\mathrm{GL}_n(\mathbb{R})$-distinguished irreducible representations of $\mathrm{GL}_n(\mathbb{C})$ when the representations are either generic or unitary. Additionally, for each such…

We give a survey of several models of irreducible complementary series representations and their limits, special representations, for the groups SU(n,1) and SO(n,1), including new ones. These groups, whose geometrical meaning is well known,…

Let $F$ be a $p$-adic field, and $K$ a quadratic extension of $F$. Using Tadic's classification of the unitary dual of $GL(n,K)$, we give the list of irreducible unitary representations of this group distinguished by $GL(n,F)$, in terms of…

We prove various results about the Local Converse Problem for split reductive groups $G$ over a non-archimedean local field~$F$ of characteristic $0$ and residual characteristic $p$. In particular, we prove that when $G$ is a symplectic or…

Let F be a non-Archimedean local field and let E be an unramified extension of F of degree n>1. To each sufficiently generic multiplicative character of E (the details are explained in the body of the paper) one can associate an irreducible…

We consider smooth representations of the unit group $G = \mathcal{A}^{\times}$ of a finite-dimensional split basic algebra $\mathcal{A}$ over a non-Archimedean local field. In particular, we prove a version of Gutkin's conjecture, namely,…

Let $F$ be a $p$-adic field ($p\neq 2$), let $E$ be a quadratic Galois extension of $F$, and let $n \geq 2$. We construct representations in the discrete spectrum of the $p$-adic symmetric space $H \backslash G$, where $G =…

Let $F$ be a local non-archimedian field of odd residue characteristic and let $G=PGL(2)$. In this paper we study an analog of irreducible cuspidal representations of the group $G(F)$ when $F$ is replaced by the field $K=F((t))$. The story…

Let $F$ be a non-discrete non-Archimedean locally compact field. In this article for a level zero Bernstein component $s$, we classify those irreducible smooth representations of ${\rm GL}_n{\integers{F}}$ (called typical representations)…

We consider the split special orthogonal group $\mathrm{SO}_{N}$ defined over a $p$-adic field. We determine the structure of any $L$-packet of $\mathrm{SO}_{N}$ containing a simple supercuspidal representation (in the sense of…

Let $G$ be a split reductive $p$-adic Lie group. This paper is the first in a series on the construction of locally analytic $G$-representations which do not lie in the principal series. Here we consider the case of the general linear group…

Let K/F be a quadratic extension of non archimedean local fields. Let V be an irreducible level zero discrete series representation of the group G = GL2(R), where R is a division algebra of center K and of index r. One assumes that V is not…

Let $F$ be a quadratic extension of $\mathbb{Q}_p$. We prove that smooth irreducible supersingular representations with central character of $\mathrm{GL}_2(F)$ are not of finite presentation.