Level-restricted paths play an important rôle 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 tableaux and rigged configurations is well-behaved with respect to level-restriction and give an explicit characterization of level-restricted rigged configurations....

We revisit the issue of counting all local fields of the restricted sine-Gordon model, in the case corresponding to a perturbation of minimal unitary conformal field theory. The problem amounts to the study of a quotient of certain space of polynomials which enter the integral representation for form factors. This space may be viewed as a q-analog of the space of conformal coinvariants associat...

We give matrices of which their determinants are the Jack polynomials expanded in terms of the monomial basis. The top row of this matrix is a list of monomial functions, the entries of the sub-diagonal are of the form −(rα + s), with r and s ∈ +, the entries above the sub-diagonal are nonnegative integers, and below all entries are 0. The quasi-triangular nature of this matrix gives a recursio...

The set of finite binary matrices a given size is known to carry type $A$ bicrystal structure. We first review this classical construction, explain how it yields short proof the equality between Kostka polynomials and one-dimensional sums together with natural generalisation $2M-X$ Pitman transform. Next, we show that, once relevant formalism on families infinite introduced, particular case muc...

This paper explains the relation between the fusion product of symmetric power sln evaluation modules, as defined by Feigin and Loktev, and the graded coordinate ring Rμ which describes the cohomology ring of the flag variety Flμ′ of GLN . The graded multiplicity spaces appearing in the decomposition of the fusion product into irreducible sln-modules are identified with the multiplicity spaces ...

The sharp bounds for the third and fourth coefficients of Ma-Minda starlike functions having fixed second coefficient are determined. These results are proved by using certain constraint coefficient problem for functions with positive real part whose coefficients are real and the first coefficient is kept fixed. Analogous results are obtained for a general class of close-to-convex functions