ID: math/0311369

An introduction to harmonic analysis on the infinite symmetric group

November 21, 2003

View on ArXiv

Similar papers 2

A central limit theorem for the characters of the infinite symmetric group and of the infinite Hecke algebra

April 30, 2011

87% Match
Pierre-Loïc Méliot
Representation Theory

In this paper, we review the representation theory of the infinite symmetric group, and we extend the works of Kerov and Vershik by proving that the irreducible characters of the infinite symmetric group always satisfy a central limit theorem. Hence, for any point of the Thoma simplex, the corresponding measures on the levels of the Young graph have a property of gaussian concentration. By using the Robinson-Schensted-Knuth algorithm and the theory of Pitman operators, we rel...

Find SimilarView on arXiv

Direct Systems of Spherical Functions and Representations

October 4, 2011

87% Match
Matthew Dawson, Gestur Olafsson, Joseph A. Wolf
Representation Theory
Differential Geometry
Functional Analysis

Spherical representations and functions are the building blocks for harmonic analysis on riemannian symmetric spaces. In this paper we consider spherical functions and spherical representations related to certain infinite dimensional symmetric spaces $G_\infty/K_\infty = \varinjlim G_n/K_n$. We use the representation theoretic construction $\phi (x) = <e, \pi(x)e>$ where $e$ is a $K_\infty$--fixed unit vector for $\pi$. Specifically, we look at representations $\pi_\infty = \...

Find SimilarView on arXiv

An introduction to the half-infinite wedge

August 31, 2013

87% Match
Rodolfo Rios-Zertuche
Representation Theory
Combinatorics
Mathematical Physics
Probability

After a quick review of the representation theory of the symmetric group, we give an exposition of the tools brought about by the so-called half-infinite wedge representation of the infinite symmetric group. We show how these can be applied to find the limit shapes of several distributions on partitions. We also briefly review the variational methods available to compute these limit shapes.

Find SimilarView on arXiv

Notes on groups and representations

August 19, 2004

87% Match
Stephen Semmes
Classical Analysis and ODEs

These informal notes concern some basic themes of harmonic analysis related to representations of groups.

Find SimilarView on arXiv

Asymptotyczna teoria reprezentacji grup permutacji (Asymptotic representation theory of symmetric groups)

April 28, 2009

86% Match
Piotr Sniady
Representation Theory

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.

Find SimilarView on arXiv

On the representations of the infinite symmetric group

March 11, 1998

86% Match
Andrei Okounkov
Representation Theory
Combinatorics

We classify all irreducible admissible representations of three Olshanski pairs connected to the infinite symmetric group. In particular, our methods yield two simple proofs of the classical Thoma's description of the characters of the infinite symmetric group. Also, we discuss a certain operation called mixture of representations which provides a uniform construction of all irreducible admissible representations.

Find SimilarView on arXiv

On semilinear representations of the infinite symmetric group

May 13, 2014

86% Match
M. Rovinsky
Representation Theory

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 field) are studied. Many results here are well-known to the experts, at least in the case of {\sl linear representations} of symmetric group. The presented results suggest, in particular, that an analogue of Hilbert's Theorem 90 should hold: i...

Find SimilarView on arXiv

Z-measures on partitions related to the infinite Gelfand pair $(S(2\infty),H(\infty))$

April 10, 2009

86% Match
Eugene Strahov
Representation Theory
Mathematical Physics

The paper deals with the z-measures on partitions with the deformation (Jack) parameters 2 or 1/2. We provide a detailed explanation of the representation-theoretic origin of these measures, and of their role in the harmonic analysis on the infinite symmetric group.

Find SimilarView on arXiv

Description of the Characters and Factor Representations of Infinite Symmetric Inverse Semigroup

February 22, 2011

85% Match
Anatoly Vershik, Pavel Nikitin
Representation Theory
Combinatorics

We give a complete list of indecomposable characters of the infinite symmetric semigroup. In comparison with the analogous list for the infinite symmetric group, one should introduce only one new parameter, which has a clear combinatorial meaning. The paper relies on the representation theory of the finite symmetric semigroups and the representation theory of the infinite symmetric group.

Find SimilarView on arXiv

Topological groups and invariant measures

October 11, 2015

85% Match
Yury A. Neretin
Functional Analysis

Lecture notes in Russian. Topics: the Haar measure (abstract theorems and explicit descriptions for different groups), measures on infinite-dimensional spaces with large natural groups of symmetries (Gaussian measures, Poisson measures, virtual permutations, inverse limits of unitary groups), zoo of examples of topological groups, generalities for large (infinite-dimensional) groups, polymorphisms.

Find SimilarView on arXiv