Pieri operators on the affine nilCoxeter algebra
@article{Berg2012PieriOO, title={Pieri operators on the affine nilCoxeter algebra}, author={Chris Berg and Franco V. Saliola and Luis G. Serrano}, journal={arXiv: Combinatorics}, year={2012} }
We study a family of operators on the affine nilCoxeter algebra. We use these operators to prove conjectures of Lam, Lapointe, Morse, and Shimozono regarding strong Schur functions.
9 Citations
Combinatorial Expansions for Families of Noncommutative k-Schur Functions
- MathematicsSIAM J. Discret. Math.
- 2014
Down operators in the affine nilCoxeter algebra are applied to yield explicit combinatorial expansions for certain families of noncommutative $k-Schur functions for a new family of $k$-Littlewood--Richardson coefficients.
The down operator and expansions of near rectangular k-Schur functions
- MathematicsJ. Comb. Theory, Ser. A
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Combinatorial description of the cohomology of the affine flag variety
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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…
Primer on k-Schur Functions
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. Associated to every complex reflection group, we construct a lattice of quotients of its braid monoid-algebra, which we term nil-Hecke algebras, and which are obtained by killing all braid words…
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- 2016
We define and study generalized nil-Coxeter algebras associated to all discrete complex reflection groups. Motivated by the Freeness Conjecture [Broue-Malle-Rouquier, 1998], we provide a complete…
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Motivated by work of Coxeter (1957), we study a class of algebras associated to Coxeter groups, which we term 'generalized nil-Coxeter algebras'. We construct the first finite-dimensional examples…
Generalized nil-Coxeter algebras over discrete complex reflection groups
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We define and study generalized nil-Coxeter algebras associated to Coxeter groups. Motivated by a question of Coxeter (1957), we construct the first examples of such finite-dimensional algebras that…
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