Combinatorial description of the cohomology of the affine flag variety

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 operato...

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Published in:Discrete mathematics and theoretical computer science Vol. DMTCS Proceedings, 28th...
Main Author: Lee, Seung Jin
Format: Journal Article Conference Proceeding
Language:English
Published: DMTCS 22.04.2020
Discrete Mathematics & Theoretical Computer Science
Subjects:
[math.math-co]mathematics [math]/combinatorics [math.co]
Combinatorics
Mathematics
ISSN:1365-8050, 1462-7264, 1365-8050
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Abstract 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 both for the affine Schubert polynomials and affine Stanley symmetric functions. This enable us to expressk-Schur functions in terms of power sum symmetric functions. We also provide the defi-nition of the affine Schubert polynomials, polynomial representatives of the Schubert basis in the cohomology of theaffine flag variety.
AbstractList 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 both for the affine Schubert polynomials and affine Stanley symmetric functions. This enable us to expressk-Schur functions in terms of power sum symmetric functions. We also provide the defi-nition of the affine Schubert polynomials, polynomial representatives of the Schubert basis in the cohomology of theaffine flag variety.
Author Lee, Seung Jin
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Snippet We construct the affine version of the Fomin-Kirillov algebra, called the affine FK algebra, to investigatethe combinatorics of affine Schubert calculus for...
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Combinatorics
Mathematics
Title Combinatorial description of the cohomology of the affine flag variety
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