Related papers: On flagged $K$-theoretic symmetric polynomials

We study the Schubert calculus of the affine Grassmannian Gr of the symplectic group. The integral homology and cohomology rings of Gr are identified with dual Hopf algebras of symmetric functions, defined in terms of Schur's P and…

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 introduce the new combinatorial approach of plethystic type of tableaux, as a method to understand coefficients of Schur functions appearing in plethysms $s_\nu[h_\lambda]$ and $s_{\nu}[e_{\lambda}]$, for any partitions $\lambda$ and…

This paper is the sequel of the paper under the same title with part 1, where we introduced refined canonical stable Grothendieck polynomials and their duals with two families of infinite parameters. In this paper we give combinatorial…

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. We examine the combinatorics of the…

We prove that the combinatorial side of the "Rational Shuffle Conjecture" provides a Schur-positive symmetric polynomial. Furthermore, we prove that the contribution of a given rational Dyck path can be computed as a certain skew LLT…

This work is a thorough investigation of skew-orthogonal polynomials with respect to a quartic Freud weight. We provide an explicit method to evaluate skew-orthogonal polynomials of any degree as linear combinations of orthogonal…

We prove an explicit combinatorial formula for certain structure constants of the T-equivariant cohomology of the flag manifold SLn/B. Our result generalizes the Pieri-type formula in ordinary cohomology proved by Sottile in 1996. Our…

We construct bosonic and fermionic eigenstates for the generalized Sutherland models associated with arbitrary reduced root systems respectively, through W-symmetrization and W-anti-symmetrization of Heckman-Opdam's nonsymmetric Jacobi…

We introduce and study a family of inhomogeneous symmetric functions which we call the Frobenius-Schur functions. These functions are indexed by partitions and differ from the conventional Schur functions in lower terms only. Our interest…

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…

Over the past years, major attention has been drawn to the question of identifying Schur-positive sets, i.e. sets of permutations whose associated quasisymmetric function is symmetric and can be written as a non-negative sum of Schur…

We provide a non-recursive, combinatorial classification of multiplicity-free skew Schur polynomials. These polynomials are $GL_n$, and $SL_n$, characters of the skew Schur modules. Our result extends work of H. Thomas--A. Yong, and C.…

The cohomology of the affine flag variety of a complex reductive group is a comodule over the cohomology of the affine Grassmannian. We give positive formulae for the coproduct of an affine Schubert class in terms of affine Stanley classes…

Grothendieck-Verdier categories (also known as $\ast$-autonomous categories) generalize rigid monoidal categories, with notable representation-theoretic examples including categories of bimodules, modules over Hopf algebroids, and modules…

We give explicit upper bounds for coefficients of polynomials appearing in Gauss-Kra\"{i}tchik formula for cyclotomic polynomials. We use a certain relation between elementary symmetric polynomials and power sums polynomials.

The K-theoretic quiver component formula expresses the K-polynomial of a type A quiver locus as an alternating sum of products of double Grothendieck polynomials. This formula was conjectured by A. Buch and R. Rim\'anyi and later proved by…

We consider Buch's rule for K-theory of the Grassmannian, in the Schur multiplicity-free cases classified by Stembridge. Using a result of Knutson, one sees that Buch's coefficients are related to Moebius inversion. We give a direct…

A new generalization of the Jack polynomials that incorporates fermionic variables is presented. These Jack superpolynomials are constructed as those eigenfunctions of the supersymmetric extension of the trigonometric…

We construct double Grothendieck polynomials of classical types which are essentially equivalent to but simpler than the polynomials defined by A.N.Kirillov in arXiv:1504.01469 and identify them with the polynomials defined by T.Ikeda and…