相关论文: Grothendieck polynomials and the Boson-Fermion cor…
Skew stable Grothendieck polynomials are $K$-theoretic analogues of skew Schur polynomials. We give a free-fermionic presentation of skew stable Grothendieck polynomials and their dual symmetric functions. By using our presentation, we…
We attempt to explain the ubiquity of tableaux and of Pieri and Cauchy formulae for combinatorially defined families of symmetric functions. We show that such formulae are to be expected from symmetric functions arising from representations…
We connect twisted vertex operator presentation of Hall-Littlewood polynomials with the action of charged free fermions, describe a boson-fermion correspondence that relates twisted vertex operators with classical Heisenberg algebra. We…
We study non-Hermitian integrable fermion and boson systems from the perspectives of Grothendieck polynomials. The models considered in this article are the five-vertex model as a fermion system and the non-Hermitian phase model as a boson…
We give a presentation of refined (dual) canonical Grothendieck polynomials and their skew versions using free-fermions. Using this, we derive a number of identities, including the skew Cauchy identities, branching rules, expansion…
In this paper, we firstly construct $\pi$-type Fermions. According to these, we define $\pi$-type Boson-Fermion correspondence which is a generalization of the classical Boson-Fermion correspondence. We can obtain $\pi$-type symmetric…
In this paper, we study Grothendieck polynomials from a combinatorial viewpoint. We introduce the factorial Grothendieck polynomials, analogues of the factorial Schur functions and present some of their properties, and use them to produce a…
Stable Grothendieck polynomials can be viewed as a K-theory analog of Schur polynomials. We extend stable Grothendieck polynomials to a two-parameter version, which we call canonical stable Grothendieck functions. These functions have the…
We give a proof of the boson-fermion correspondence (an isomorphism of lattice and fermion vertex algebras) in terms of isomorphism of factorization spaces.
The differential equation for Boltzmann's function is replaced by the corresponding discrete finite difference equation. The difference equation is, then, symmetrized so that the equation remains invariant when step d is replaced by -d. The…
We study the algebraic properties of plethystic vertex operators, introduced in J. Phys. A: Math. Theor. 43 405202 (2010), underlying the structure of symmetric functions associated with certain generalized universal character rings of…
The Clifford algebra of the endomorphisms of the exterior algebra of a countably dimensional vector space induces natural bosonic shadows, i.e. families of linear maps between the cohomologies of complex grassmannians. The main result of…
We give an algebraic (non-analytic) proof of the deformed boson-fermion Fock space construction of Molev's double supersymmetric Schur functions, among other results, from our previous paper. In other words, we make no assumptions on the…
We present an application of the Grassmann algebra to the problem of the monomer-dimer statistics on a two-dimensional square lattice. The exact partition function, or total number of possible configurations, of a system of dimers with a…
We find a close correspondence between certain partition functions of ideal quantum gases and certain symmetric polynomials. Due to this correspondence it can be shown that a number of thermodynamic identities which have recently been…
A Lie theoretic interpretation is given for some formulas of Schur functions and Schur $Q$-functions. Two realizations of the basic representation of the Lie algebra $A^{(2)}_2$ are considered; one is on the fermionic Fock space and the…
The structure of filtered algebras of Grothendieck's differential operators of truncated polynomials in one variable and graded Poisson algebras of their principal symbols is explicitly determined. A related infinitesimal-birational duality…
We introduce and study several combinatorial properties of a class of symmetric polynomials from the point of view of integrable vertex models in finite lattice. We introduce the $L$-operator related with the $U_q(sl_2)$ $R$-matrix, and…
The topology of two-dimensional movement allows for existing of anyons -- particles obeying statistics intermediate between that of bosons and fermions. In this article, the functional form of the occupation numbers of free anyons is…
The classical Grothendieck inequality is viewed as a statement about representations of functions of two variables over discrete domains by integrals of two-fold products of functions of one variable. An analogous statement is proved,…