Related papers: Littlewood--Richardson coefficients and integrable…
We study the Kronecker product of two Schur functions $s_\lambda\ast s_\mu$, defined as the image of the characteristic map of the product of two $S_n$ irreducible characters. We prove special cases of a conjecture of Monical--Tokcan--Yong…
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…
We exhibit a weight-preserving bijection between semi-standard Young tableaux and semi-skyline augmented fillings to provide a combinatorial proof that the Schur functions decompose into nonsymmetric functions indexed by compositions. The…
We prove recursive formulas for sums of squares and sums of triangular numbers in terms of sums of divisors functions and we give a variety of consequences of these formulas. Intermediate applications include statements about positivity of…
Partition functions often become \tau-functions of integrable hierarchies, if they are considered dependent on infinite sets of parameters called time variables. The Hurwitz partition functions Z = \sum_R…
We present a program that allows for the computation of tensor products of irreducible representations of Lie algebras A-G based on the explicit construction of weight states. This straightforward approach (which is slower and more…
We prove Fredholm determinants build out from generalizations of Schur measures, or equivalently, arbitrary multiplicative statistics of the original Schur measures are tau-functions of the 2D Toda lattice hierarchy. Our result apply to…
We establish a fundamental connection between the geometric RSK correspondence and GL(N,R)-Whittaker functions, analogous to the well known relationship between the RSK correspondence and Schur functions. This gives rise to a natural family…
We prove an explicit formula for the tensor product with itself of an irreducible complex representation of the symmetric group defined by a rectangle of height two. We also describe part of the decomposition for the tensor product of…
We present relations between Hirota-type bilinear operators, scalar products on spaces of symmetric functions and integrals defining matrix model partition functions. Using the fermionic Fock space representation, a proof of the expansion…
In this paper, we study the tensor product of two unitary irreducible representations, as well as the tensor product of a unitary irreducible representation with a finite-dimensional one, and determine the corresponding Clebsch-Gordan…
A remarkable feature of Schur functions -- the common eigenfunctions of cut-and-join operators from $W_\infty$ -- is that they factorize at the peculiar two-parametric topological locus in the space of time-variables, what is known as the…
Using a finite-dimensional Clifford algebra a new combinatorial product formula for the small quantum cohomology ring of the complex Grassmannian is presented. In particular, Gromov-Witten invariants can be expressed through certain…
We give a positive equivariant Littlewood-Richardson rule also discovered independently by Molev. Our proof generalizes a proof by Stembridge of the ordinary Littlewood-Richardson rule. We describe a weight-preserving bijection between our…
The manuscript reviews Dirichlet Series of important multiplicative arithmetic functions. The aim is to represent these as products and ratios of Riemann zeta-functions, or, if that concise format is not found, to provide the leading…
We define and study rational discrete analytic functions and prove the existence of a coisometric realization for discrete analytic Schur multipliers.
We determine the necessary and sufficient combinatorial conditions for which the tensor product of two irreducible polynomial representations of $GL(n,\mathbb{C})$ is isomorphic to another. As a consequence we discover families of…
We provide a generalization of the Littlewood identity, both sides of which are related to alternating sign matrices. The classical Littlewood identity establishes a nice product formula for the sum of all Schur polynomials. Compared to the…
We study two different one-parameter generalizations of Littlewood--Richardson coefficients, namely Hall polynomials and generalized inverse Kostka polynomials, and derive new combinatorial formulae for them. Our combinatorial expressions…
A driving question in (quantum) cohomology of flag varieties is to find non-recursive, positive combinatorial formulas for expressing the product of two classes in a particularly nice basis, called the Schubert basis. Bertram,…