author={Luc Lapointe and Jennifer Morse},
  journal={Transactions of the American Mathematical Society},
  • L. Lapointe, J. Morse
  • Published 28 January 2005
  • Mathematics
  • Transactions of the American Mathematical Society
We prove that structure constants related to Hecke algebras at roots of unity are special cases of k-Littlewood-Richardson coefficients associated to a product of k-Schur functions. As a consequence, both the 3-point Gromov-Witten invariants appearing in the quantum cohomology of the Grassmannian, and the fusion coefficients for the WZW conformal field theories associated to su(l) are shown to be k-Littlewood-Richardson coefficients. From this, Mark Shimozono conjectured that the k-Schur… 
Quantum cohomology of G/P and homology of affine Grassmannian
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Applying parabolic Peterson: affine algebras and the quantum cohomology of the Grassmannian
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The main purpose of this paper is to show that the multiplication of a Schubert polynomial of finite type $A$ by a Schur function can be understood from the multiplication in the space of dual
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Crystal approach to affine Schubert calculus
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Schubert polynomials for the affine Grassmannian
Let G be a complex simply connected simple group and K a maximal compact subgroup. Let F = C((t)) denote the field of formal Laurent series and O = C[[t]] the ring of formal power series. The
The nil Hecke ring and cohomology of G/P for a Kac-Moody group G.
A ring R is constructed, which is very simply and explicitly defined as a functor of W together with the W-module [unk] alone and such that all these four structures on H(*)(G/B) arise naturally from the ring R.
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Abstract: 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
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AbstractThe k-Young lattice Yk is a weak subposet of the Young lattice containing partitions whose first part is bounded by an integer k > 0. The Yk poset was introduced in connection with
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This monograph, now in its second revised edition, provides a systematic treatment of topological quantum field theories in three dimensions, inspired by the discovery of the Jones polynomial of