# 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
- 2013

Combinatorial description of the cohomology of the affine flag variety

- MathematicsDiscrete Mathematics & Theoretical Computer Science
- 2020

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

- Mathematics
- 2014

The purpose of this chapter is to outline some of the results and open problems related to k-Schur functions, mostly in the setting of symmetric function theory. This chapter roughly follows the…

The lattice of nil-Hecke algebras over real and complex reflection groups

- Mathematics
- 2021

. 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…

On the classification of finite-dimensional nil-Coxeter algebras over complex reflection groups

- Mathematics
- 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…

Generalized nil-Coxeter algebras

- Mathematics
- 2018

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

- Mathematics
- 2016

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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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…

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