Related papers: Orthosymplectic Cauchy identities

Using the vertex operator representations for symplectic and orthogonal Schur functions, we define two families of symmetric functions and show thatthey are the skew symplectic and skew orthogonal Schur polynomials defined implicitly by…

Vertex operator realizations of symplectic and orthogonal Schur functions are studied and expanded. New proofs of determinant identities of irreducible characters for the symplectic and orthogonal groups are given. We also give a new proof…

Motivated by statistical applications, this paper introduces Cauchy identities for characters of the compact classical groups. These identities generalize the well-known Cauchy identity for characters of the unitary group, which are Schur…

We define a measure on tuples of partitions, called the symplectic Schur process, that should be regarded as the right analogue of the Schur process of Okounkov-Reshetikhin for the Cartan type C. The weights of our measure include factors…

We show, using either Fock space techniques or Macdonald difference operators, that certain symplectic and orthogonal analogues of Okounkov's Schur measure are determinantal with kernels given by explicit double contour integrals. We give…

We introduce two vertex operators to realize skew odd orthogonal characters $so_{\lambda/\mu}(x^{\pm})$ and derive the Cauchy identity for the skew characters via Toeplitz-Hankel-type determinant similar to the Schur functions. The method…

There exist a number of well known multiplicative generating functions for series of Schur functions. Amongst these are some related to the dual Cauchy identity whose expansion coefficients are rather simple, and in some cases periodic in…

The Rogers-Ramanujan identities are investigated using the Cauchy identity for Schur functions.

A series of bilinear identities on the Schur symmetric functions is obtained with the use of Pluecker relations.

Symmetric Grothendieck polynomials are analogues of Schur polynomials in the K-theory of Grassmannians. We build dual families of symmetric Grothendieck polynomials using Schur operators. With this approach we prove skew Cauchy identity and…

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…

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…

The Cauchy identities play an important role in the theory of symmetric functions. It is known that Cauchy sums for the $q$-Whittaker and the skew Schur polynomials produce the same factorized expressions modulo a $q$-Pochhammer symbol. We…

We consider pairs of a set-valued column-strict tableau and a reverse plane partition of the same shape. We introduce algortithms for them, which implies a bijective proof for the finite sum Cauchy identity for Grothendieck polynomials and…

We solve the multiplicative Cauchy functional equation on symmetric cones with respect to two different multiplication algorithms. We impose no regularity assumptions on respective functions.

In the article [11] of L. Kunyansky a symmetric integral identity for Bessel functions of the first and second kind was proved in order to obtain an explicit inversion formula for the spherical mean transform where our data is given on the…

The identities satisfied by two-dimensional chiral quantum fields are studied from the point of view of vertex algebras. The Cauchy-Jacobi identity (or the Borcherds identity) for three mutually local fields is proved and consequently a…

The (dual) Cauchy identity has an easy algebraic proof utilising a commutation relation between the up and (dual) down operators. By using Fomin's growth diagrams, a bijective proof of the commutation relation can be "bijectivised" to…

The Cauchy identity gives a recipe for decomposing a double Grothendieck polynomial $\mathfrak{G}^{(\beta)}_w(x;y)$ as a sum of products $\mathfrak{G}^{(\beta)}_v(x)\mathfrak{G}^{(\beta)}_u(y)$ of single Grothendieck polynomials.…

We give another proof for the (-1)-enumeration of self-complementary plane partitions with at least one odd side-length by specializing a certain Schur function identity. The proof is analogous to Stanley's proof for the ordinary…