Affine Yangian and 3-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

W-symmetry, topological vertex and affine Yangian

We discuss the representation theory of the non-linear chiral algebra W1+∞ of Gaberdiel and Gopakumar and its connection to the Yangian of û(1) whose presentation was given by Tsymbaliuk. The characters of completely degenerate representations of W1+∞ are given by the topological vertex. The Yangian picture provides an infinite number of commuting charges which can be explicitly diagonalized in...

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...