Related papers: Character theory approach to Sato-Tate groups

The survey presents the main developments obtained over the last decade regarding pointwise ergodic theorems for measure preserving actions of locally compact groups. The survey includes an exposition of the solutions to a number of long…

The distribution of species body size within taxonomic groups exhibits a heavy right-tail extending over many orders of magnitude, where most species are significantly larger than the smallest species. We provide a simple model of…

We study the behavior of Galois periods under the local theta correspondence for even orthogonal and symplectic groups. Specifically, we compare their multiplicities and construct explicit transfer maps. Furthermore, we establish both an…

Standard high-dimensional factor models assume that the comovements in a large set of variables could be modeled using a small number of latent factors that affect all variables. In many relevant applications in economics and finance,…

The problem of filtering - propagation of states through stochastic differential equations (SDEs) and association of measurement data using Bayesian inference - in a state space which forms a Lie group is considered. Particular emphasis is…

The increasing availability of time --and space-- resolved data describing human activities and interactions gives insights into both static and dynamic properties of human behavior. In practice, nevertheless, real-world datasets can often…

We describe a novel algorithm for random sampling of freely reduced words equal to the identity in a finitely presented group. The algorithm is based on Metropolis Monte Carlo sampling. The algorithm samples from a stretched Boltzmann…

Following Arthur's study of the representations of the orthogonal and symplectic groups, we prove many cases of both the local and global Arthur conjectures for tempered representations of the unitary group. This completes the proof of…

Let C denote the Fermat curve over Q of prime exponent l. The Jacobian Jac(C) of C splits over Q as the product of Jacobians Jac(C_k), 0< k < l-1, where C_k are curves obtained as quotients of C by certain subgroups of automorphisms of C.…

Let X be a locally compact Abelian group. We consider linear forms of independent random variables with values in X. In doing so, one of the coefficients of the linear forms is a random variable with a Bernoulli distribution. For some…

In this survey, we report on the state of the art of some of the fundamental problems in the Lie theory of Lie groups modeled on locally convex spaces, such as integrability of Lie algebras, integrability of Lie subalgebras to Lie…

By studying lattices of normal subgroups, especially those of the socle and radical, an expression is obtained for the minimal number of conjugacy classes required to generate a group. This number is shown to be captured by the character…

A new Bayesian modelling framework is introduced for piece-wise homogeneous variable-memory Markov chains, along with a collection of effective algorithmic tools for change-point detection and segmentation of discrete time series. Building…

This is an introductory level survey of some topics from a new branch of fractal analysis -- the theory of self-similar groups. We discuss recent works on random walks on self-similar groups and their applications to the problem of…

Free cumulants are nice and useful functionals of the shape of a Young diagram, in particular they give the asymptotics of normalized characters of symmetric groups S(n) in the limit n\to\infty. We give an explicit combinatorial formula for…

The purpose of this article is to give an exposition of topological properties of spaces of homomorphisms from certain finitely generated discrete groups to Lie groups $G$, and to describe their connections to classical representation…

The conditional tail average treatment effect (CTATE) is defined as a difference between the conditional tail expectations of potential outcomes, which can capture heterogeneity and deliver aggregated local information on treatment effects…

We derive several identities that feature irreducible characters of the general linear, the symplectic, the orthogonal, and the special orthogonal groups. All the identities feature characters that are indexed by shapes that are "nearly"…

Conventional survival analysis approaches estimate risk scores or individualized time-to-event distributions conditioned on covariates. In practice, there is often great population-level phenotypic heterogeneity, resulting from (unknown)…

Let $k$ be an infinite finitely generated field of characteristic $p>0$. Fix a separated scheme $X$ smooth, geometrically connected, and of finite type over $k$ and a smooth proper morphism $f:Y\rightarrow X$. The main result of this paper…