相关论文: Markov measures on Young tableaux and induced repr…

We study the representations of the infinite symmetric group induced from the identity representations of Young subgroups. It turns out that such induced representations can be either of type~I or of type~II. Each Young subgroup corresponds…

The goal of the paper is to describe new connections between representation theory and algebraic combinatorics on one side, and probability theory on the other side. The central result is a construction, by essentially algebraic tools, of a…

The new approach to the theory of complex representrations of the finite symmetric groups which based on the notions of Coxeter generators., Gelfand-Zetlin algebras, Hecke algebra, Young-Jucys-Murphi generators and which hardly used…

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…

We start with definitions of the general notions of the theory of $\Bbb Z_{2}$-graded algebras. Then we consider theory of inductive families of $\Bbb Z_{2}$-graded semisimple finite-dimensional algebras and its representations in the…

In this article, we classify disconnected reductive groups over an algebraically closed field with a few caveats. Internal parts of our result are both a classification of finite groups and a classification of integral representations of a…

We give a new (inductive) proof of the classical Frobenius--Young correspondence between irreducible complex representations of the symmetric group and Young diagrams, using the new approach, suggested in \cite{OV, VO}, to determining this…

We will introduce the notion of inductive limits of compact quantum groups as $W^*$-bialgebras equipped with some additional structures. We also formulate their unitary representation theories. Those give a more explicit…

We obtain a complete classification of the continuous unitary representations of oligomorphic permutation groups (those include the infinite permutation group $S_\infty$, the automorphism group of the countable dense linear order, the…

We construct a four-parameter family of Markov processes on infinite Gelfand-Tsetlin schemes that preserve the class of central (Gibbs) measures. Any process in the family induces a Feller Markov process on the infinite-dimensional boundary…

The Gelfand-Tsetlin graph is an infinite graded graph that encodes branching of irreducible characters of the unitary groups. The boundary of the Gelfand-Tsetlin graph has at least three incarnations --- as a discrete potential theory…

The classification results for the extreme characters of two basic "big" groups, the infinite symmetric group S(infinity) and the infinite-dimensional unitary group U(infinity), are remarkably similar. It does not seem to be possible to…

We show that any twisted Dijkgraaf-Witten representation of a mapping class group of an orientable, compact surface with boundary has finite image. This generalizes work of Etingof, Rowell and Witherspoon showing that the braid group images…

We extend work of McKay, Morse, and Wilf by giving exact formulas and asymptotic formulas for the number of skew Young tableaux T in two situations: (1) the "inside shape" and total number of cells of T are fixed, and (2) the inside shape…

The paper consists of two parts. The first part introduces the representation ring for the family of compact unitary groups U(1), U(2),.... This novel object is a commutative graded algebra R with infinite-dimensional homogeneous…

In this paper we study the possibility to define irreducible representations of the symmetric groups with the help of finitely many relations. The existence of finite bases is established for the classes of representations corresponding to…

This is an introduction to the group algebras of the symmetric groups, written for a quarter-long graduate course. After recalling the definition of group algebras (and monoid algebras) in general, as well as basic properties of…

We investigate representations of mapping class groups of surfaces that arise from the untwisted Drinfeld double of a finite group G, focusing on surfaces without marked points or with one marked point. We obtain concrete descriptions of…

A "2-group" is a category equipped with a multiplication satisfying laws like those of a group. Just as groups have representations on vector spaces, 2-groups have representations on "2-vector spaces", which are categories analogous to…

We study asymptotics of reducible representations of the symmetric groups S_q for large q. We decompose such a representation as a sum of irreducible components (or, alternatively, Young diagrams) and we ask what is the character of a…