In this paper, we present a simple combinatorial proof of a Weyl type formula for hook Schur polynomials, which has been obtained by using a Kostant type cohomology formula for glm|n. In general, we can obtain in a combinatorial way a Weyl type formula for various highest weight representations of a Lie superalgebra, which together with a general linear algebra forms a Howe dual pair.

In this paper we present a comparison of the service disciplines in real-time queueing systems (the customers have a deadline before which they should enter the service booth). We state that the more a service discipline gives priority to customers having an early deadline, the least the average stationary lateness is. We show this result by comparing adequate random vectors with the Schur-Conv...

In this paper, using a relation between Schur multipliers of pairs and triples of groups, the fundamental group and homology groups of a homotopy pushout of Eilenberg-MacLane spaces, we present among other things some behaviors of Schur multipliers of pairs and triples with respect to free, amalgamated free, and direct products and also direct limits of groups with topological approach.

We introduce and discuss Jones pairs. These provide a generalization and a new approach to the four-weight spin models of Bannai and Bannai. We show that each four-weight spin model determines a “dual” pair of association schemes. 1. Jones Pairs The space of k × k matrices acts on itself in three distinct ways: if C ∈ Mk(F), we can define endomorphisms XC , ∆C and YC by XC(M) = CM, ∆C(M) = C ◦M...

The pair of groups, symmetric group S2n and hyperoctohedral group Hn , form a Gelfand pair. The characteristic map is a mapping from the graded algebra generated by the zonal spherical functions of (S2n, Hn) into the ring of symmetric functions. The images of the zonal spherical functions under this map are called the zonal polynomials. A wreath product generalization of the Gelfand pair (S2n, ...

The Pieri rule expresses the product of a Schur function and a single row Schur function in terms of Schur functions. We extend the classical Pieri rule by expressing the product of a skew Schur function and a single row Schur function in terms of skew Schur functions. Like the classical rule, our rule involves simple additions of boxes to the original skew shape. Our proof is purely combinator...

In this paper, we consider the boundedness of the Libera operator on Dirichlet spaces in terms of the Schur test. Moreover, we get its point spectrum and norm.

Recent work of A. Postnikov shows that cylindric skew Schur functions, which are a generalisation of skew Schur functions, have a strong connection with a problem of considerable current interest: that of finding a combinatorial proof of the non-negativity of the 3-point Gromov-Witten invariants. After explaining this motivation, we study cylindric skew Schur functions from the point of view of...