Related papers: Symmetric group characters as symmetric functions
We study the remarkable Saxl conjecture which states that tensor squares of certain irreducible representations of the symmetric groups S_n contain all irreducibles as their constituents. Our main result is that they contain representations…
This paper presents a noncommutative theory of symmetric functions, based on the notion of quasi-determinant. We begin with a formal theory, corresponding to the case of symmetric functions in an infinite number of independent variables.…
Highlighting the use of critical classes, we consider constituents in Kronecker products, in particular of spin characters of the double covers of the symmetric and alternating groups. We apply results from the spin case to find…
The notion of spherically symmetric superfunctions as functions invariant under the orthosymplectic group is introduced. This leads to dimensional reduction theorems for differentiation and integration in superspace. These spherically…
We present a computational approach to studying the structure of the representation ring of the symmetric group in dimension six. The Kronecker coefficients and all power formulae of irreducible representations of $S_6$ are computed using…
In math.CO/0109093 the author obtained a formula for the value of an irreducible symmetric group character indexed by a partition of rectangular shape. In the present paper this formula is (conjecturally) generalized to arbitrary shapes.
Using an algorithm for computing the symmetric function Kronecker product of D-finite symmetric functions we find some new Kronecker product identities. The identities give closed form formulas for trace-like values of the Kronecker…
We construct a generalization of the theory of symmetric functions involving functions of commuting and anticommuting (Grassmannian) variables. These new functions, called symmetric functions in superspace, are invariant under the diagonal…
We construct modules of the $0$-Hecke algebra whose images under the quasisymmetric characteristic map are the Young row-strict quasisymmetric Schur functions. This provides a representation-theoretic interpretation of this basis of…
The classical algebra $\Lambda$ of symmetric functions has a remarkable deformation $\Lambda^*$, which we call the algebra of shifted symmetric functions. In the latter algebra, there is a distinguished basis formed by shifted Schur…
We give a new formula for the irreducible spin characters of the symmetric groups. This formula is analogous to Stanley's character formula for the usual (linear) characters of the symmetric groups.
In the paper, properties of antisymmetric orbit functions are reviewed and further developed. Antisymmetric orbit functions on the Euclidean space $E_n$ are antisymmetrized exponential functions. Antisymmetrization is fulfilled by a Weyl…
The theory of noncommutative Schur functions can be used to obtain positive combinatorial formulae for the Schur expansion of various classes of symmetric functions, as shown by Fomin and Greene. We develop a theory of noncommutative super…
For polynomial representations of $GL_n$ of a fixed degree, H. Krause defined a new internal tensor product using the language of strict polynomial functors. We show that over an arbitrary commutative base ring $k$, the Schur functor…
We define a number of related combinatorial objects, each of which possesses a surprising symmetry. We include several applications such as a combinatorial explanation for certain fixed points of the involution $\omega$ on the ring of…
We establish, for the character table of the symmetric group, the positivity of the row sums indexed by irreducible characters, when restricted to various subsets of the conjugacy classes. A notable example is that of partitions with all…
In this paper we obtain the complete description of all indecomposable characters (central positive-definite functions) of inductive limits of the symmetric groups under block diagonal embedding. As a corollary we obtain the full…
We introduce a ring of noncommutative shifted symmetric functions based on an integer-indexed sequence of shift parameters. Using generating series and quasideterminants, this multiparameter approach produces deformations of the ring of…
Given an positive integer $k$, let $n:=\binom{k+1}{2}$. In 2012, during a talk at UCLA, Jan Saxl conjectured that all irreducible representations of the symmetric group $S_n$ occur in the decomposition of the tensor square of the…
We introduce the multiple zeta functions with structures similar to those of symmetric functions such as Schur $P$-, Schur $Q$-, symplectic and orthogonal functions in the representation theory. We first consider their basic properties such…