# 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} }

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…

## 63 Citations

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 We prove an unpublished result of D. Peterson which states that the quantum cohomology QH*(G/P) of a flag…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

- MathematicsJournal 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…

Schubert Polynomials and $k$-Schur Functions

- MathematicsElectron. J. Comb.
- 2014

It is shown that the multiplication of a SchUbert polynomial of finite type $A$ by a Schur function, which is referred to as Schubert vs. Schur problem, can be understood from the multiplication in the space of dual $k$-Schur functions.

Crystal approach to affine Schubert calculus

- Mathematics
- 2016

Author(s): Morse, Jennifer; Schilling, Anne | Abstract: We apply crystal theory to affine Schubert calculus, Gromov-Witten invariants for the complete flag manifold, and the positroid stratification…

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