Related papers: The Horn recursion for Schur P- and Q- functions: …

The Kronecker coefficients and the Littlewood-Richardson coefficients are nonnegative integers depending on three partitions. By definition, these coefficients are the multiplicities of the tensor product decomposition of two irreducible…

The reduced Schur functions are studied. Their relations to the basic representation of $A^(1)_{r-1}$ and modular representations of the symmetric groups are clarified. Littlewood-Richardson coefficients appear in the linear relations among…

The necessary and sufficient Horn inequalities which determine the non-vanishing Littlewood-Richardson coefficients in the cohomology of a Grassmannian are recursive in that they are naturally indexed by non-vanishing Littlewood-Richardson…

This note is an extended abstract of my talk at the workshop on Representation Theory and Symmetric Functions, MSRI, April 14, 1997. We discuss the problem of finding an explicit description of the semigroup $LR_r$ of triples of partitions…

A new combinatorial approach to the ribbon tableaux generating functions and q-Littlewood Richardson coefficients of Lascoux, Leclerc and Thibon is suggested. We define operators which add ribbons to partitions and following Fomin and…

In this paper we explicitly compute all Littlewood-Richardson coefficients for semisimple or Kac-Moody groups G, that is, the structure coefficients of the cohomology algebra H^*(G/P), where P is a parabolic subgroup of G. These…

We provide direct proofs of product and coproduct formulae for Schur functions where the coefficients (Littlewood--Richardson coefficients) are defined as counting puzzles. The product formula includes a second alphabet for the Schur…

The classical Littlewood-Richardson rule is a rule for computing coefficients in many areas, and comes in many guises. In this paper we prove two Littlewood-Richardson rules for symmetric skew quasisymmetric Schur functions that are…

While equality of skew Schur functions is well understood, the problem of determining when two skew Schur $Q$ functions are equal is still largely open. It has been studied in the case of ribbon shapes in 2008 by Barekat and van…

Littlewood Richardson coefficients are structure constants appearing in the representation theory of the general linear groups ($GL_n$). The main results of this paper are: 1. A strongly polynomial randomized approximation scheme for…

The Littlewood-Richardson (LR) coefficient counts among many other things the LR tableaux of a given shape and a given content. We prove, that the number of LR tableaux weakly increases if one adds to the shape and the content the shape and…

We first describe a system of inequalities (Horn's inequalities) that characterize eigenvalues of sums of Hermitian matrices. When we apply this system for integral Hermitian matrices, one can directly test it by using Littlewood-Richardson…

We show that the Littlewood-Richardson coefficients are values at 1 of certain parabolic Kazhdan-Lusztig polynomials for affine symmetric groups. These q-analogues of Littlewood-Richardson multiplicities coincide with those previously…

The Newell-Littlewood numbers $N_{\mu,\nu,\lambda}$ are tensor product multiplicities of Weyl modules for classical Lie groups, in the stable limit. For which triples of partitions $(\mu,\nu,\lambda)$ does $N_{\mu,\nu,\lambda}>0$ hold? The…

We use Hopf algebras to prove a version of the Littlewood-Richardson rule for skew Schur functions, which implies a conjecture of Assaf and McNamara. We also establish skew Littlewood-Richardson rules for Schur P- and Q-functions and…

We relate noncommutative Littlewood-Richardson coefficients of Bessenrodt-Luoto-van Willigenburg to classical Littlewood-Richardson coefficients via crystal reflection operators. A key role is played by the combinatorics of frank words.

We give a new formula for the Littlewood--Richardson coefficients in terms of peelable tableaux compatible with shuffle tableaux, in the same fashion as Remmel--Whitney rule. This gives an efficient way to compute generalized…

In this paper, we construct the q-analogue of Poirier-Reutenauer algebras, related deeply with other q-combinatorial Hopf algebras. As an application, we use them to realize the odd Schur functions defined in \cite{EK}, and naturally obtain…

We give a Littlewood-Richardson type rule for expanding the product of a row-strict quasisymmetric Schur function and a symmetric Schur function in terms of row-strict quasisymmetric Schur functions. This expansion follows from several new…

In previous work with Mikhail Khovanov and Aaron Lauda we introduced two odd analogues of the Schur functions: one via the combinatorics of Young tableaux (odd Kostka numbers) and one via the odd symmetrization operator. In this paper we…