Affine dual equivalence and $k$-Schur functions

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.

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...

Shifted Dual Equivalence and Schur P -positivity

Dual equivalence puts a crystal-like structure on linear representations of the symmetric group that affords many nice combinatorial properties. In this talk, we extend this theory to type B, putting an analogous structure on projective representations of the symmetric group. On the level of generating functions, the type A theory gives a universal method for proving Schur positivity, and the t...