Related papers: Bilinear identities on Schur symmetric functions

Gurevich, Pyatov and Saponov recently stated an expansion for the product of two Schur functions and gave a proof based on the Pluecker relations. Here we show that this identity is in fact a special case of a quite general Schur function…

In this paper we establish two symmetric identities on sums of products of Euler polynomials.

For the Schur polynomials bounded and unbounded generalizations of the Cauchy identities are found.

We present a set of algebraic relations among Schur functions which are a multi-time generalization of the ``discrete Hirota relations'' known to hold among the Schur functions of rectangular partitions. We prove the relations as an…

Schur functions satisfy the relative Pl\"ucker relations which describe the projective embedding of the flag varieties and the Hirota bilinear equations for the modified KP hierarchies. These relative Pl\"ucker relations are generalized to…

We prove bilinear virial identities for the nonlinear Schrodinger equation, which are extensions of the Morawetz interaction inequalities. We recover and extend known bilinear improvements to Strichartz inequalities and provide applications…

In this paper, using the theory of category, we generalize known properties of symmetric polynomials and functions and characterize the multi-indicial symmetric functions. Examples have been given on Schur functions.

We consider an operator of Bernstein for symmetric functions, and give an explicit formula for its action on an arbitrary Schur function. This formula is given in a remarkably simple form when written in terms of some notation based on the…

An identity is derived expressing Schur functions as sums over products of pairs of Schur $Q$-functions, generalizing previously known special cases. This is shown to follow from their representations as vacuum expectation values (VEV's) of…

We derive several symmetric identities for Bernoulli and Euler polynomials which imply some known identities. Our proofs depend on the new technique developed in part I and some identities obtained in [European J. Combin. 24(2003),…

We present some thoughts on the relation between symmetric Schur-class functions on the bidisk and Schur-class functions on the symmetrized bidisk. Among other things, use of this relation leads to a finite dimensional realization result…

In this paper we introduce doubly symmetric functions, arising from the equivalence of particular linear combinations of Schur functions and hook Schur functions. We study algebraic and combinatorial aspects of doubly symmetric functions,…

Grothendieck's inequalities for operators and bilinear forms imply some factorization results for complex m x n matrices. Based on the theory of operator spaces and completely bounded mappings we present norm optimal versions of these…

In this paper, we study some symmetric identities of q-Euler numbers and polynomials. From these properties, we derive several identities of q-Euler numbers and polynomials.

We prove a version of the Hodge-Riemann bilinear relations for Schur polynomials of K\"ahler forms and for Schur polynomials of positive forms on a complex vector space.

Analogues of classical combinatorial identities for elementary and homogeneous symmetric functions with coefficients in Yanigian are discussed. As a corollary, similar relations are deduced for shifted Schur functions.

We obtain general identities for the product of two Schur functions in the case where one of the functions is indexed by a rectangular partition, and give their t-analogs using vertex operators. We study subspaces forming a filtration for…

This paper is devoted to the proof of boundedness of bilinear smooth square functions. Moreover, we deduce boundedness of some bilinear pseudo-differential operators associated with symbols belonging to a subclass of $BS^0_{0,0}$.

A systematic procedure for generating certain identities involving elementary symmetric functions is proposed. These identities, as particular cases, lead to new identities for binomial and q-binomial coefficients.

Some new identities for Schur functions are proved. In particular, we settle in the affirmative a recent conjecture of Ishikawa-Wakayama and solve a problem raised by Bressoud.