By the properties of Schur-convex function, Schur geometrically convex function and Schur harmonically convex function, Schur-convexity, Schur geometric and Schur harmonic convexities of the dual form for a class of symmetric functions are simply proved. As an application, several inequalities are obtained, some of which extend the known ones. Mathematics subject classification (2010): 26D15, 0...

An important problem in algebraic combinatorics is finding expansions of products of symmetric functions as sums of symmetric functions. Schur functions form a well-known basis for the ring of symmetric functions. The Littlewood-Richardson rule was introduced to expand the product of two Schur functions as a positive sum of Schur functions. Remmel and Whitney introduced an algorithmic way to fi...

In this paper, using the properties of Schur-convex function, Schur-geometrically convex function and Schur-harmonically convex function, we provide much simpler proofs of the Schur-convexity, Schur-geometric convexity and Schur-harmonic convexity for a composite function of the complete symmetric function.

We prove lower bounds for the worst case error of quadrature formulas that use given sample points Xn={x1,…,xn}. are mainly interested in optimal point sets Xn, but also hold with high probability independently and uniformly distributed points. As a tool, we recent result (and extensions thereof) Vybíral on positive semi-definiteness certain matrices related to product theorem Schur. The new te...

This paper can be considered as a continuation of a survey article on the representation theory of nite general linear groups in non describing characteristic D4]. The main theme there as well as in the present paper is the connection between the representation theory of quantum GL n and the non describing characteristic case for general linear groups. This connection is given through certain t...

John Stembridge [St] has recently solved the important problem of finding a “Littlewood-Richardson rule” for Q-functions. His proof is very natural combinatorially, but lengthy, if all the background is included. It uses extensive material from Worley’s thesis [W] and Sagan’s similar theory of shifted tableaux [Sa]. To include this result in a forthcoming book (coauthored by John Humphreys), an...

We introduce a quasisymmetric generalization of Berele and Regev’s hook Schur functions and prove that these new quasisymmetric hook Schur functions decompose the hook Schur functions in a natural way. In this paper we examine the combinatorics of the quasisymmetric hook Schur functions, providing analogues of the RobinsonSchensted-Knuth algorithm and a generalized Cauchy Identity. Résumé. Nous...

Recently a new basis for the Hopf algebra of quasisymmetric functions QSym, called quasisymmetric Schur functions, has been introduced by Haglund, Luoto, Mason, van Willigenburg. In this paper we extend the definition of quasisymmetric Schur functions to introduce skew quasisymmetric Schur functions. These functions include both classical skew Schur functions and quasisymmetric Schur functions ...

Our main result provides a closed expression for the completely bounded Fourier multiplier norm of the spherical functions on the generalized Lorentz groups SO0(1, n) (for n ≥ 2). As a corollary, we find that there is no uniform bound on the completely bounded Fourier multiplier norm of the spherical functions on the generalized Lorentz groups. We extend the latter result to the groups SU(1, n)...