Related papers: Descent sets for symplectic groups

This article (written in Polish) is aimed for a wide mathematical audience. It is intended as an introductory text concerning problems of the asymptotic theory of symmetric groups.

A general setting to study a certain type of formulas, expressing characters of the symmetric group $\mathfrak{S}_n$ explicitly in terms of descent sets of combinatorial objects, has been developed by two of the authors. This theory is…

The classical theta correspondence, based on the Weil representation, allows one to lift automorphic representations on symplectic groups or their double covers to automorphic representations on special orthogonal groups. It is of interest…

In this note we show that similar to the classical case the ring of representations of symmetric groups in a tensor derived category is certain ring of symmetric functions. We also show that in the general setting considered here, the Adams…

In this note the smooth (i.e. with open stabilizers) linear and {\sl semilinear} representations of certain permutation groups (such as infinite symmetric group or automorphism group of an infinite-dimensional vector space over a finite…

The aim of the paper is to give a full classification of factorizations of groups in terms of descent cohomology (pointed) sets introduced in [5]. We show that descent cohomology includes Serre's non-abelian group cohomology as a special…

We define a cocycle on the group of symplectic diffeomorphisms of a symplectic manifold and investigate its properties. The main applications are concerned with symplectic actions of discrete groups. For example, we give an alternative…

The purpose of this note is to announce an extension of the descent method of Ginzburg, Rallis and Soudry to the setting of essentially self dual representations. This extension of the descent construction provides a complement to recent…

We show that diagrammatic sets, a topologically sound alternative to polygraphs and strict $\omega$-categories, admit an internal notion of equivalence in the sense of coinductive weak invertibility. We prove that equivalences have the…

Symmetry plays a fundamental role in understanding natural phenomena and mathematical structures. This work develops a comprehensive theory for studying the persistent symmetries and degree of asymmetry of finite point configurations over…

In this paper, we develop a representation-theoretic formulation of discrete-time linear systems. We show that such systems are naturally viewed as representations of time groups acting on vector spaces, thereby endowing the state space…

Motivated by the properties of the descent polynomials, which enumerate permutations of $S_n$ with a fixed descent set, we define descent polynomials for labeled rooted trees. We give recursive and explicit formulas for these polynomials…

The branching theorem expresses irreducible character values for the symmetric group $S_n$ in terms of those for $S_{n-1}$, but it gives the values only at elements of $S_n$ having a fixed point. We extend the theorem by providing a…

Motivated by the study of periods of automorphic forms and relative trace formulae, we develop the theory of descent necessary to study orbital integrals arising in the fundamental lemma for a general class of symmetric spaces over a…

We study the modular representation theory of the symmetric and alternating groups. One of the most natural ways to label the irreducible representations of a given group or algebra in the modular case is to show the unitriangularity of the…

The isotropic harmonic oscillator in N dimensions is shown to have an underlying symmetry group O(2,1)X O(N)which implies a unique result for the energy spectrum of the system. Raising and lowering operators analogous to those of the…

We study asymptotics of random shifted Young diagrams which correspond to a given sequence of reducible projective representations of the symmetric groups. We show limit results (Law of Large Numbers and Central Limit Theorem) for their…

We start with a small paradigm shift about group representations, namely the observation that restriction to a subgroup can be understood as an extension-of-scalars. We deduce that, given a group $G$, the derived and the stable categories…

The number of alternating runs is a natural permutation statistic. We show it can be used to define some commutative subalgebras of the symmetric group algebra, and more precisely of the descent algebra. The Eulerian peak algebras naturally…

In this note we give a self-contained proof of the following classification (up to conjugation) of subgroups of the general symplectic group of dimension n over a finite field of characteristic l, for l at least 5, which can be derived from…