Related papers: Symmetric group representations and Z

In 2015, the author proved combinatorially character formulas expressing sums of the (formal) dimensions of irreducible representations of symplectic groups, refining some works of Nekrasov and Okounkov, Han, King, and Westbury. In this…

If $G$ is a second countable locally compact Hausdorff groupoid with Haar system, we show that every representation induced from an irreducible representation of a stability group is irreducible.

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…

We classify irreducible representations of the special linear groups in positive characteristic with small weight multiplicities with respect to the group rank and give estimates for the maximal weight multiplicities. For the natural…

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…

A fundamental problem in the representation theory of the symmetric group, Sn, is to describe the coefficients in the decomposition of a tensor product of two simple representations. These coefficients are known in the literature as the…

In a recent paper, the authors introduced a new basis of the ring of symmetric functions which evaluate to the irreducible characters of the symmetric group at roots of unity. The structure coefficients for this new basis are the stable…

For any finite group $G$ and any prime $p$ one can ask which ordinary irreducible representations remain irreducible in characteristic $p$. We answer this question for $p=2$ when $G$ is a proper double cover of the symmetric group. Our…

The representation theory for categorical groups is constructed. Each categorical group determines a monoidal bicategory of representations. Typically, these categories contain representations which are indecomposable but not irreducible. A…

We study the representation theory of the infinite type A Hecke algebra over a non-archimedean field in the case where the parameter is a pseudo-uniformizer. Specifically, we consider a family of representations, called almost-symmetric,…

The aim of the present paper is to obtain a classification of all the irreducible modular representations of the symmetric group on $n$ letters of dimension at most $n^3$, including dimension formulae. This is achieved by improving an idea,…

We complete the classification of the finite dimensional irreducible representations of finite W-algebras associated to even multiplicity nilpotent elements in classical Lie algebras. This extends earlier work where this classification is…

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…

Representation theory of finite groups portrays a marvelous crossroad of group theory, algebraic combinatorics, and probability. In particular the Plancherel measure is a probability that arises naturally from representation theory, and in…

We prove certain polynomial relations between the values of complex irreducible characters of general finite symmetric groups. We use it to find some sets of conjugacy classes such that no finite symmetric group has a complex irreducible…

Let $n$ be a positive integer, and let $\rho_n = (n, n-1, n-2, \ldots, 1)$ be the ``staircase'' partition of size $N = {n+1 \choose 2}$. The Saxl conjecture asserts that every irreducible representation $S^\lambda$ of the symmetric group…

It is a well known fact from the group theory that irreducible tensor representations of classical groups are suitably characterized by irreducible representations of the symmetric groups. However, due to their different nature, vector and…

Infinite statistics in which all representations of the symmetric group can occur is known as a special case of quon theory. Our previous work has built a relativistic quantum field theory which allows interactions involving infinite…

The article presents the results of experiments in computation of statistical values related to Young diagrams, including the estimates on maximum and average (by Plancherel distribution) dimension of irreducible representation of symmetric…

We classify irreducible representations of connected compact Lie groups whose orbit space is isometric to the orbit space of a representation of a finite extension of (positive dimensional) toric group. They turn out to be exactly the…