Related papers: Class expansion of some symmetric functions in Juc…
In this paper, we study the relationship between polynomial integrals on the unitary group and the conjugacy class expansion of symmetric functions in Jucys-Murphy elements. Our main result is an explicit formula for the top coefficients in…
The problem of computing the class expansion of some symmetric functions evaluated in Jucys-Murphy elements appears in different contexts, for instance in the computation of matrix integrals. Recently, M. Lassalle gave a unified algebraic…
In this note we define a generalization of Hall-Littlewood symmetric functions using formal group law and give an elementary proof of the generating function formula for the generalized Hall-Littlewood symmetric functions. We also give some…
We use derived Hall algebra of the category of nilpotent representations of Jordan quiver to reconstruct the theory of symmetric functions, focusing on Hall-Littlewood symmetric functions and various operators acting on them.
We exhibit a vertex operator which implements multiplication by power-sums of Jucys-Murphy elements in the centers of the group algebras of all symmetric groups simultaneously. The coefficients of this operator generate a representation of…
We study symmetric polynomials whose variables are odd-numbered Jucys-Murphy elements. They define elements of the Hecke algebra associated to the Gelfand pair of the symmetric group with the hyperoctahedral group. We evaluate their…
A connection is made between complete homogeneous symmetric polynomials in Jucys-Murphy elements and the unitary Weingarten function from random matrix theory. In particular we show that $h_r(J_1,...,J_n),$ the complete homogeneous…
In this paper we consider asymptotic expansions for a class of sequences of symmetric functions of many variables. Applications to classical and free probability theory are discussed.
A novel polynomial expansion method of symmetric Boolean functions is described. The method is efficient for symmetric Boolean function with small set of valued numbers and has the linear complexity for elementary symmetric Boolean…
We derive an explicit sum formula for symmetric Macdonald polynomials. Our expression contains multiple sums over the symmetric group and uses the action of Hecke generators on the ring of polynomials. In the special cases $t=1$ and $q=0$,…
This paper is about a family of symmetric rational functions that form a one-parameter generalization of the classical Hall-Littlewood polynomials. We introduce two sets of (skew and non-skew) functions that are akin to P and Q…
A method for computing integrals of polynomial functions on compact symmetric spaces is given. Those integrals are expressed as sums of functions on symmetric groups.
We study symmetric function analogues of the higher order Bell numbers. Their construction involves iterated plethystic exponential towers mimicking the single variable exponential generating functions for the higher order Bell numbers. We…
We develop the general theory of Jack-Laurent symmetric functions, which are certain generalisations of the Jack symmetric functions, depending on an additional parameter p_0.
We express the topological expansion of the Jacobi Unitary Ensemble in terms of triple monotone Hurwitz numbers. This completes the combinatorial interpretation of the topological expansion of the classical unitary invariant matrix…
We provide a combinatorial description of the coefficients appearing in the expansion of Hall-Littlewood polynomials in terms of monomial symmetric functions. We also give a Littlewood-Richardson rule for Hall-Littlewood polynomials. For…
In this paper, we look at the number of factorizations of a given permutation into star transpositions. In particular, we give a natural explanation of a hidden symmetry, answering a question of I.P. Goulden and D.M. Jackson. We also have a…
We give an elementary proof of the development of Macdonald polynomials in terms of "modified complete" and elementary symmetric functions.
A cluster expansion is proposed, that applies to both continuous and discrete systems. The assumption for its convergence involves an extension of the neat Kotecky-Preiss criterion. Expressions and estimates for correlation functions are…
We give the explicit analytic development of Macdonald polynomials in terms of "modified complete" and elementary symmetric functions. These expansions are obtained by inverting the Pieri formula. Specialization yields similar developments…