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arXiv · 2610.01708

$K$-$k$-Schur functions are $k$-Schur positive

Haojun Bai·Peter L. Guo
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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.

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Haojun Bai, Peter L. Guo. 2026-10-01. $K$-$k$-Schur functions are $k$-Schur positive. https://arxiv.org/abs/2610.01708

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