Combinatorial description of the cohomology of the affine flag variety

@article{Lee2020CombinatorialDO,
  title={Combinatorial description of the cohomology of the affine flag variety},
  author={Seung Jin Lee},
  journal={Discrete Mathematics \& Theoretical Computer Science},
  year={2020}
}
  • Seung Jin Lee
  • Published 8 June 2015
  • Mathematics
  • Discrete Mathematics & Theoretical Computer Science
International audience We construct the affine version of the Fomin-Kirillov algebra, called the affine FK algebra, to investigatethe combinatorics of affine Schubert calculus for typeA. We introduce Murnaghan-Nakayama elements and Dunklelements in the affine FK algebra. We show that they are commutative as Bruhat operators, and the commutativealgebra generated by these operators is isomorphic to the cohomology of the affine flag variety. As a byproduct, weobtain Murnaghan-Nakayama rules… 
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