Related papers: Fermionic formula for double Kostka polynomials

It is proved a $BMO$-estimation for quadratic partial sums of two-dimensional Fourier series from which it is derived an almost everywhere exponential summability of quadratic partial sums of double Fourier series.

Here we propose a way to construct generalized Kostka polynomials. Namely, we construct an equivariant filtration on tensor products of irreducible representations. Further, we discuss properties of the filtration and the adjoint graded…

We prove a duality formula for certain sums of values of poly-Bernoulli polynomials which generalizes dualities for poly-Bernoulli numbers. We first compute two types of generating functions for these sums, from which the duality formula is…

We prove a conjecture of Lecouvey, which proposes a closed, positive combinatorial formula for symplectic Kostka-Foulkes polynomials, in the case of rows of arbitrary weight. To show this, we construct a new algorithm for computing…

An algebraic iterative formula for the spin Kostka-Foulkes polynomial $K^-_{\xi\mu}(t)$ is given using vertex operator realizations of Hall-Littlewood symmetric functions and Schur's Q-functions. Based on the operational formula, more…

In this paper we prove a conjectured modular equation of Farkas and Kra, which involving a half sum of certain modular form of weight $1$ for congruence subgroup $\Gamma_1(k)$ with any prime $k$. We prove that their conjectured identity…

We give a formula for the q-characters of arbitrary highest-weight integrable modules of sl_{r+1} as a linear combination of the fermionic q-characters of special fusion products of integrable modules. The coefficients in the sum are…

We propose an $r$-variable version of Kostka-Shoji polynomials $K^-_{\lambda\mu}$ for $r$-multipartitions $\lambda,\mu$. Our version has positive integral coefficients and encodes the graded multiplicities in the space of global sections of…

Macdonald superpolynomials provide a remarkably rich generalization of the usual Macdonald polynomials. The starting point of this work is the observation of a previously unnoticed stability property of the Macdonald superpolynomials when…

The main theorem here is the K-theoretic analogue of the cohomological `stable double component formula' for quiver functions in [Knutson, Miller, and Shimozono, math.AG/0308142]. This K-theoretic version is still in terms of lacing…

We consider multiple sums and multi-integrals as tau functions of the BKP hierarchy using neutral fermions as the simplest tool for deriving these. The sums are over projective Schur functions $Q_\alpha$ for strict partitions $\alpha$. We…

We prove a generalization of the Verlinde formula to fermionic rational conformal field theories. The fusion coefficients of the fermionic theory are equal to sums of fusion coefficients of its bosonic projection. In particular, fusion…

A new explicit closed-form formula for the multivariate $(n, k)$th partial Bell polynomial $B_{n,k} (x_1, x_2, ..., x_{n - k + 1})$ is deduced. The formula involves multiple summations and makes it possible, for the first time, to easily…

We discuss a product formula for $F$-polynomials in cluster algebras, and provide two proofs. One proof is inductive and uses only the mutation rule for $F$-polynomials. The other is based on the Fock-Goncharov decomposition of mutations.…

Recent work of Borwein, Choi, and the second author examined a collection of polynomials closely related to the Goldbach conjecture: the polynomial $F_N$ is divisible by the $N$th cyclotomic polynomial if and only if there is no…

We prove a generalization of the Kibble--Slepian formula (for Hermite polynomials) and its unitary analogue involving the $2$D Hermite polynomials recently proved in \cite{Ism4}. We derive integral representations for the $2$D Hermite…

In this article I consider type II superstring in the pure spinor formulation with constant background fields in the context of T-dualization. First I prove that bosonic and fermionic T-dualization commute using already known T-dual…

Level-restricted paths play an important role in crystal theory. They correspond to certain highest weight vectors of modules of quantum affine algebras. We show that the recently established bijection between Littlewood--Richardson…

If $[\lambda(j)]$ is a multipartition of the positive integer $n$ (a sequence of partitions with total size $n$), and $\mu$ is a partition of $n$, we study the number $K_{[\lambda(j)]\mu}$ of sequences of semistandard Young tableaux of…

We give a combinatorial proof of the skew Kostka analogue of the K-saturation theorem. More precisely, for any positive integer k, we give an explicit injection from the set of skew semistandard Young tableaux with skew shape…