Year: 2026
Type: preprint
Abstract: The $k$-Schur functions (resp., $K$-$k$-Schur functions) are the symmetric function representatives of Schubert classes in the homology (resp., $K$-homology) of the affine Grassmannian of type $A$. We prove that every $K$-$k$-Schur function is a nonnegative integer linear combination in the basis of $k$-Schur functions. This settles a conjecture by Lam, Schilling and Shimozono. The proof relies on realizations of $k$-Schur and $K$-$k$-Schur functions as Catalan and Katalan functions, respectively.
Source: arXiv (Cornell University)
Authors: Bai, Haojun, Guo, Peter L.
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7215755824