Related papers: Symmetric Jack polynomials from non-symmetric theo…

There are representations of the type-A Hecke algebra on spaces of polynomials in anti-commuting variables. Luque and the author [S\'em. Lothar. Combin. 66 (2012), Art. B66b, 68 pages, arXiv:1106.0875] constructed nonsymmetric Macdonald…

There is a space of vector-valued nonsymmetric Jack polynomials associated with any irreducible representation of a symmetric group. Singular polynomials for the smallest singular values are constructed in terms of the Jack polynomials. The…

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…

In this note, a deep connection between free field realisations of conformal field theories and symmetric polynomials is presented. We give a brief introduction into the necessary prerequisites of both free field realisations and symmetric…

In this paper we introduce and investigate a one-parameter family of polynomials. They are semisymmetric, i.e. symmetric in the variables with odd and even index separately. In fact, the family forms a basis of the space of semisymmetric…

This paper describes how many known graph polynomials arise from the coefficients of chromatic symmetric function expansions in different bases, and studies a new polynomial arising by expanding over a basis given by chromatic symmetric…

We study the coefficients in the expansion of Jack polynomials in terms of power sums. We express them as polynomials in the free cumulants of the transition measure of an anisotropic Young diagram. We conjecture that such polynomials have…

We consider a deformation of Kerov character polynomials, linked to Jack symmetric functions. It has been introduced recently by M. Lassalle, who formulated several conjectures on these objects, suggesting some underlying combinatorics. We…

Two evaluation formulas are derived for the Jack superpolynomials. The evaluation formulas are expressed in terms of products of fillings of skew diagrams. One of these formulas is nothing but the evaluation formula of the Jack polynomials…

In this paper, we develop the theory of symmetric triads with multiplicities. First, we classify abstract symmetric triads with multiplicities. Second, we determine the symmetric triads with multiplicities corresponding to commutative…

The Jack symmetric polynomials $P_\lambda^{(\alpha)}$ form a class of symmetric polynomials which are indexed by a partition $\lambda$ and depend rationally on a parameter $\alpha$. They reduced to the Schur polynomials when $\alpha=1$, and…

A new generalization of the Jack polynomials that incorporates fermionic variables is presented. These Jack superpolynomials are constructed as those eigenfunctions of the supersymmetric extension of the trigonometric…

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.…

In the intersection of the theories of nonsymmetric Jack polynomials in $N$ variables and representations of the symmetric groups $\mathcal{S}_{N}$ one finds the singular polynomials. For certain values of the parameter $\kappa$ there are…

In this note we prove an explicit binomial formula for Jack polynomials and discuss some applications of it.

We study Jack polynomials in $N$ variables, with parameter $\alpha$, and having a prescribed symmetry with respect to two disjoint subsets of variables. For instance, these polynomials can exhibit a symmetry of type AS, which means that…

This paper contains the proof of difference counterparts of the conjectures due to Keven Kadell on symmetric and anti-symmetric Macdonald polynomials.

We present a positivity conjecture for the coefficients of the development of Jack polynomials in terms of power sums. This extends Stanley's ex-conjecture about normalized characters of the symmetric group. We prove this conjecture for…

Vector-valued Jack polynomials associated to the symmetric group ${\mathfrak S}_N$ are polynomials with multiplicities in an irreducible module of ${\mathfrak S}_N$ and which are simultaneous eigenfunctions of the Cherednik-Dunkl operators…

In a recent work, we have initiated the theory of N=2 symmetric superpolynomials. As far as the classical bases are concerned, this is a rather straightforward generalization of the N=1 case. However this construction could not be…