相关论文: New fermionic formula for unrestricted Kostka poly…
Fermionic-type character formulae are presented for charged irreduciblemodules of the graded parafermionic conformal field theory associated to the coset $osp(1,2)_k/u(1)$. This is obtained by counting the weakly ordered `partitions'…
We propose a method to prove a polyhedral branching formula for Kirillov-Reshetikhin (KR) modules over a quantum affine algebra. When the underlying simple Lie algebra is of exceptional type, such a formula remains conjectural in many…
A lattice Wess-Zumino model is formulated on the basis of Ginsparg-Wilson fermions. In perturbation theory, our formulation is equivalent to the formulation by Fujikawa and Ishibashi and by Fujikawa. Our formulation is, however, free from a…
Kostka-Foulkes polynomials are Lusztig's $q$-analogues of weight multiplicities for irreducible representations of semisimple Lie algebras. It has long been known that these polynomials have non-negative coefficients. A statistic on…
In this paper, we extend work of the first author on a crystal structure on rigged configurations of simply-laced type to all non-exceptional affine types using the technology of virtual rigged configurations and crystals. Under the…
In this paper, we seek to prove the equality of the $q$-graded fermionic sums conjectured by Hatayama et al. in its full generality, by extending the results of Di Francesco and Kedem to the non-simply laced case. To this end, we will…
We obtain an explicit combinatorial formula for certain parabolic Kostka-Shoji polynomials associated with the cyclic quiver, generalizing results of Shoji and of Liu and Shoji.
In this paper we present a new formula for the number of unrestricted partitions of $n$. We do this by introducing a correspondence between the number of unrestrited partitions of $n$ and the number of non-negative solutions of systems of…
We compute $t$--analogs of $q$--characters of all $l$--fundamental representations of the quantum affine algebras of type $E_6^{(1)}$, $E_7^{(1)}$, $E_8^{(1)}$ by a supercomputer. In particular, we prove the fermionic formula for…
A thorough account is given of the derivation of uniform semiclassical approximations to the particle and kinetic energy densities of N noninteracting bounded fermions in one dimension. The employed methodology allows the inclusion of…
We obtain the fermionic formulas for the characters of (k, r)-admissible configurations in the case of r=2 and r=3. This combinatorial object appears as a label of a basis of certain subspace $W(\Lambda)$ of level-$k$ integrable highest…
We establish fractional Leibniz rules in weighted settings for nonnegative self-adjoint operators on spaces of homogeneous type. Using a unified method that avoids Fourier transforms, we prove bilinear estimates for spectral multiplier on…
The effective formulas reducing the two-dimensional Hermite polynomials to the classical (one-dimensional) orthogonal polynomials are given. New one-parameter generating functions for these polynomials are derived. Asymptotical formulas for…
Costa et al. [Phys. Rev. Lett. 123, 151601 (2019)] recently gave a general solution to the anomaly equations for $n$ charges in a $U(1)$ gauge theory. `Primitive' solutions of chiral fermion charges were parameterised and it was shown how…
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…
We show that the only polynomial sets with a generating function of the form F (xt -- R(t)) and satisfying a three-term recursion relation are the monomial set and the rescaled ultraspherical, Hermite, and Chebyshev polynomials of the first…
In this paper, we give an alternative proof for the asymptotic stability of solitons for nonlinear Schr\"odinger equations with internal modes. The novel idea is to use "refined profiles" developed by the authors for the analysis of small…
We prove that the number of distinct homotopy types of limits of one-parameter semi-algebraic families of closed and bounded semi-algebraic sets is bounded singly exponentially in the additive complexity of any quantifier-free first order…
We use Kashiwara-Nakashima's combinatorics of crystal graphs associated to the roots sytems $B_{n}$ and $D_{n}$ to extend the results of \QCITE{cite}{}{lec3} and \QCITE{cite}{}{Mor} by showing that Morris type recurrence formulas also exist…
We prove ratio asymptotic for sequences of multiple orthogonal polynomials with respect to a Nikishin system of measures ${\mathcal{N}}(\sigma_1,...,\sigma_m)$ such that for each $k$, the support of $\sigma_k$ consists of an interval…