Canonical Decompositions of Affine Permutations, Affine Codes, and Split $k$-Schur Functions

Canonical Decompositions of Affine Permutations, Affine Codes, and Split k-Schur Functions

We develop a new perspective on the unique maximal decomposition of an arbitrary affine permutation into a product of cyclically decreasing elements, implicit in work of Thomas Lam [Lam06]. This decomposition is closely related to the affine code, which generalizes the kbounded partition associated to Grassmannian elements. We also prove that the affine code readily encodes a number of basic co...

Affine dual equivalence and k-Schur functions

The k-Schur functions were first introduced by Lapointe, Lascoux and Morse [18] in the hopes of refining the expansion of Macdonald polynomials into Schur functions. Recently, an alternative definition for k-Schur functions was given by Lam, Lapointe, Morse, and Shimozono [17] as the weighted generating function of starred strong tableaux which correspond with labeled saturated chains in the Br...

1 k - Schur functions and affine Schubert calculus

Expansions of k-Schur Functions in the Affine nilCoxeter Algebra

We give a type free formula for the expansion of k-Schur functions indexed by fundamental coweights within the affine nilCoxeter algebra. Explicit combinatorics are developed in affine type C.

Tableaux on k+1-cores, reduced words for affine permutations, and k-Schur expansions

The k-Young lattice Y k is a partial order on partitions with no part larger than k. This weak subposet of the Young lattice originated [9] from the study of the k-Schur functions s (k) λ , symmetric functions that form a natural basis of the space spanned by homogeneous functions indexed by k-bounded partitions. The chains in the k-Young lattice are induced by a Pieri-type rule experimentally ...