Related papers: On cuspidality of global Arthur packets for symple…

We provide a complete asymptotic distribution theory for clustered data with a large number of independent groups, generalizing the classic laws of large numbers, uniform laws, central limit theory, and clustered covariance matrix…

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…

Let $G$ be a simple group over a global function field $K$, and let $\pi$ be a cuspidal automorphic representation of $G$. Suppose $K$ has two places $u$ and $v$ (satisfying a mild restriction on the residue field cardinality), at which the…

The investigation of universality questions for local eigenvalue statistics continues to be a driving force in the theory of Random Matrices. For Matrix Models [53] the method of orthogonal polynomials can be used and the asymptotics of the…

An algebraic description of basic discrete symmetries (space inversion P, time reversal T, charge conjugation C and their combinations PT, CP, CT, CPT) is studied. Discrete subgroups {1,P,T,PT} of orthogonal groups of multidimensional…

Global control offers a promising route to scalable quantum computing. A recent conjecture by Hu et al. (arXiv:2508.19075) proposes that any connected qubit graph equipped with global Ising-type interactions and tunable global transverse…

In this paper we prove Vogan's conjecture on Arthur packets for general linear groups over $p$-adic fields, building on earlier work. The proof uses a special case of endoscopic lifting, adapted from the 1992 book by Adams, Barbasch and…

Consider the family of automorphic representations on a unitary group with cohomological factor $\pi_0$ at infinity and given split level. We compute statistics of this family as the level goes to infinity. For unramified unitary groups and…

We classify the automorphic representations (over number fields) and the irreducible admissible representations (over local fields) of unitary groups which are not quasi-split, under the assumption that the same is known for quasi-split…

Let F be a totally real number field, n a prime integer, and G a unitary group of rank n defined over F that is compact at every infinite place. We prove an asymptotic formula for the number of cuspidal automorphic representations of G…

In this paper we study abstract group homomorphisms between the groups of rational points of linear algebraic groups which are not necessarily reductive. One of our main goal is to obtain results on homomorphisms from the groups of rational…

In the framework of algebraic quantum field theory we analyze the anomalous statistics exhibited by a class of automorphisms of the observable algebra of the two-dimensional free massive Dirac field, constructed by fermionic gauge group…

We provide a family of representations of GL(2n) over a p-adic field that admit a non-vanishing linear functional invariant under the symplectic group (i.e. representations that are Sp(2n)- distinguished). While our result generalizes a…

We study a topological space obtained from a graph via replacing vertices with smooth Riemannian manifolds, i.e. a decorated graph. We construct a semiclassical asymptotics of the solutions of Cauchy problem for a time-dependent…

We provide a systematic description of the automorphism groups of specially cocompact CAT(0) cube complexes. We show that these groups are topologically finitely generated, present a method to explicitly obtain generating sets, and prove a…

We present a conjecture (and a proof for G=SL(2)) generalizing a result of J. Arthur which expresses a character value of a cuspidal representation of a $p$-adic group as a weighted orbital integral of its matrix coefficient. It also…

In this paper, we prove the closure ordering conjecture on the local $L$-parameters of representations in local Arthur packets of $\mathrm{G}_n=\mathrm{Sp}_{2n}, \mathrm{SO}_{2n+1}$ over a non-Archimedean local field of characteristic zero.…

We propose a notion of cusp forms on semisimple symmetric spaces. We then study the real hyperbolic spaces in detail, and show that there exists both cuspidal and non-cuspidal discrete series. In particular, we show that all the spherical…

The unitary representation theory of locally compact contraction groups and their semi-direct products with $\mathbb{Z}$ is studied. We put forward the problem of completely characterising such groups which are type I or CCR and this…

In the first part of this paper we study minimal representations of simply connected simple split groups of type $D_k$ or $E_k$ over local non-archimedian fields. Our main result is an explicit formula for the spherical vectors in these…