# QUANTUM COHOMOLOGY AND THE k-SCHUR BASIS

```@article{Lapointe2007QUANTUMCA,
title={QUANTUM COHOMOLOGY AND THE k-SCHUR BASIS},
author={Luc Lapointe and Jennifer Morse},
journal={Transactions of the American Mathematical Society},
year={2007},
volume={360},
pages={2021-2040}
}```
• 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
• Mathematics
• 2007
Let G be a simple and simply-connected complex algebraic group, P ⊂ G a parabolic subgroup. We prove an unpublished result of D. Peterson which states that the quantum cohomology QH*(G/P) of a flag
k-SHAPE POSET AND BRANCHING OF k-SCHUR FUNCTIONS
• Mathematics
• 2010
We give a combinatorial expansion of a Schubert homology class in the affine Grassmannian GrSLk into Schubert homology classes in GrSLk+1 . This is achieved by studying the combinatorics of a new
Applying parabolic Peterson: affine algebras and the quantum cohomology of the Grassmannian
• Mathematics
Journal of Combinatorics
• 2019
The Peterson isomorphism relates the homology of the affine Grassmannian to the quantum cohomology of any flag variety. In the case of a partial flag, Peterson's map is only a surjection, and one
Schubert polynomials and \$k\$-Schur functions (Extended abstract)
• Mathematics
• 2013
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
k-Schur expansions of Catalan functions
• Mathematics
• 2020
K-theoretic Catalan functions
• Mathematics
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