Related papers: A reciprocal branching problem for automorphic rep…

Similarly to how the classical group ring isomorphism problem asks, for a commutative ring $R$, which information about a finite group $G$ is encoded in the group ring $RG$, the twisted group ring isomorphism problem asks which information…

We study irreducibility of Galois representations $\rho_{\pi,\lambda}$ associated to a $n=7$ or 8-dimensional regular algebraic essentially self-dual cuspidal automorphic representation $\pi$ of $\text{GL}_n(\mathbb{A}_\mathbb{Q})$. We show…

We study branching multiplicity spaces of complex classical groups in terms of GL(2) representations. In particular, we show how combinatorics of GL(2) representations are intertwined to make branching rules under the restriction of GL(n)…

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…

In this paper we formulate and study the problem of representing groups on graphs. We show that with respect to polynomial time turing reducibility, both abelian and solvable group representability are all equivalent to graph isomorphism,…

Let $G$ denote the unramified quasi-split unitary group $\mathbb{U}(1,1)(F)$ over a $p$-adic field $F$ with residual characteristic $p \neq 2$. In this article, we determine the branching rules for all irreducible supercuspidal…

The ordering of scalar fields after a phase transition in which a group $G$ of global symmetries is spontaneously broken to a subgroup $H$ provides a possible explanation for the origin of structure in the universe, as well as leading to…

Let $V$ be a finite dimensional complex vector space and $W\subset \GL(V)$ be a finite complex reflection group. Let $V^{\reg}$ be the complement in $V$ of the reflecting hyperplanes. A classical conjecture predicts that $V^{\reg}$ is a…

We study the unitary boundary representation of a strongly transitive group acting on a right-angled hyperbolic building. We show its irreducibility. We do so by associating to such a representation a representation of a certain Hecke…

Every representation of the Cuntz algebra $\mathcal{O}_n$ leads to a unitary representation of the Higman-Thompson group $V_n$. We consider the family $\{\pi_x\}_{x\in [0,1[}$ of permutative representations of $\mathcal{O}_n$ that arise…

Let G be a real or complex linear algebraic reductive group. Let H and F be reductive subgroups. We study the natural H action on G/F. The main theorem of this note shows that generic H orbits are closed. This theorem is then applied to…

Let $G=\operatorname{O}(1,n+1)$ with maximal compact subgroup $K$ and let $\Pi$ be a unitary irreducible representation of $G$ with non-trivial $(\mathfrak{g},K)$-cohomology. Then $\Pi$ occurs inside a principal series representation of…

An interesting class of orthogonal representations consists of the so-called turn-regular ones, i.e., those that do not contain any pair of reflex corners that "point to each other" inside a face. For such a representation H it is possible…

We consider several questions about restriction of representations of classical and metaplectic groups over local and global fields to subgroups, extending considerably the scope of the earlier work on $SO(n),SO(n-1)$. This includes Bessel…

We give a complete description of the discrete spectra in the branching law $\Pi|_{G'}$ with respect to the pair $(G,G')=(O(p,q), O(p',q') \times O(p'',q''))$ for irreducible unitary representations $\Pi$ of $G$ that are "geometric…

A real representation $\pi$ of a finite group may be regarded as a homomorphism to an orthogonal group $\Or(V)$. For symmetric groups $S_n$, alternating groups $A_n$, and products $S_n \times S_{n'}$ of symmetric groups, we give criteria…

Let $E/F$ be a CM extension of number fields, and let $H < G$ be a unitary Gan--Gross--Prasad pair defined with respect to $E/F$ that is compact at infinity. We consider a family $\mathcal{F}$ of automorphic representations of $G \times H$…

Obtaining sparse, interpretable representations of observable data is crucial in many machine learning and signal processing tasks. For data representing flows along the edges of a graph, an intuitively interpretable way to obtain such…

We study the conjugacy problem in cyclic extensions of free groups. It is shown that the conjugacy problem is solvable in split extensions of finitely generated free groups by virtually inner automorphisms. An algorithm for construction of…

For reductive groups $G$ over a number field we discuss automorphic liftings from cuspidal irreducible automorphic representations $\pi$ of $G(\mathbb{A})$ to cuspidal irreducible automorphic representations on $H(\mathbb{A})$ for the…