Anne Schilling

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We define a bijection from Littlewood–Richardson tableaux to rigged configurations and show that it preserves the appropriate statistics. This proves in particular a quasi-particle expression for the generalized Kostka polynomials KλR(q) labeled by a partition λ and a sequence of rectangles R. The generalized Kostka polynomials are q-analogues of(More)
We present and prove Rogers–Schur–Ramanujan (Bose/Fermi) type identities for the Virasoro characters of the minimal model M(p, p). The proof uses the continued fraction decomposition of p/p introduced by Takahashi and Suzuki for the study of the Bethe’s Ansatz equations of the XXZ model and gives a general method to construct polynomial generalizations of(More)
Kerov, Kirillov, and Reshetikhin defined a bijection between highest weight vectors in the crystal graph of a tensor power of the vector representation, and combinatorial objects called rigged configurations, for type A (1) n . We define an analogous bijection for all nonexceptional affine types, thereby proving (in this special case) the fermionic formulas(More)
Kirillov and Reshetikhin conjectured what is now known as the fermionic formula for the decomposition of tensor products of certain finite dimensional modules over quantum affine algebras. This formula can also be extended to the case of q-deformations of tensor product multiplicities as recently conjectured by Hatayama et al.. In its original formulation(More)
General fermionic expressions for the branching functions of the rational coset conformal field theories ŝu(2)M × ŝu(2)N/ŝu(2)M+N are given. The equality of the bosonic and fermionic representations for the branching functions is proven by introducing polynomial truncations of these branching functions which are the configuration sums of the RSOS models in(More)
We study the Schubert calculus of the affine Grassmannian Gr of the symplectic group. The integral homology and cohomology rings of Gr are identified with dual Hopf algebras of symmetric functions, defined in terms of Schur’s P and Q functions. An explicit combinatorial description is obtained for the Schubert basis of the cohomology of Gr, and this is(More)
In 1979, Norton showed that the representation theory of the 0-Hecke algebra admits a rich combinatorial description. Her constructions rely heavily on some triangularity property of the product, but do not use explicitly that the 0-Hecke algebra is a monoid algebra. The thesis of this paper is that considering the general setting of monoids admitting such(More)