Macdonald defined in [M1] a remarkable class of symmetric polynomials Pλ(x; q, t) which depend on two parameters and interpolate between many families of classical symmetric polynomials. For example Pλ(x; t) = Pλ(x; 0, t) are the Hall-Littlewood polynomials which themselves specialize for t = 0 to Schur functions sλ. Also Jack polynomials arise by taking q = t and letting t tend to 1. The Hall-...

CONTENTS Introduction 1 1. Notation 3 2. Main definitions and first properties 4 3. Cohomology of line bundles and generalised Kostka-Foulkes polynomials 5 4. The little adjoint module and short q-analogues 11 5. Short Hall-Littlewood polynomials 18 6. Miscellaneous remarks 23 References 25 INTRODUCTION Let G be a semisimple algebraic group with Lie algebra g. We consider generalisations of Lus...

We give a complete description of the graded multiplicity space which appears in the Feigin-Loktev fusion product [FL99] of graded Kirillov-Reshetikhin modules for all simple Lie algebras. This construction is used to obtain an upper bound formula for the fusion coefficients in these cases. The formula generalizes the case of g = Ar [AKS06], where the multiplicities are generalized Kostka polyn...

This paper contains the generalization of the Feigin-Stoyanovsky construction to all integrable sl r+1-modules. We give formulas for the q-characters of any highest-weight integrable module of sl r+1 as a linear combination of the fermionic q-characters of the fusion products of a special set of integrable modules. The coefficients in the sum are the entries of the inverse matrix of generalized...

The combinatorial properties of Young modules corresponding to maximal Young subgroups are studied: an explicit formula for p-Kostka numbers is given, and as applications, the ordinary characters of Young modules are described and a branching rule for Young modules is determined. Moreover, for certain n-part partitions the reduction formulas for p-Kostka numbers given in A. Henke, S. Koenig [Re...

We obtain an explicit combinatorial formula for certain parabolic Kostka-Shoji polynomials associated with the cyclic quiver, generalizing results of Shoji and Liu Shoji.