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. This decomposition is closely related to the affine code, which generalizes the $k$-bounded partition associated to Grassmannian elements. We also prove that …