In 2020, Morse, Blasiak, and Seelinger introduced the K-theoretic Catalan functions as motivated by the search for a K-theoretic counterpart to the relationship between k-Schur structure constants and the complete flag variety. The authors conjectured that a subfamily, the closed k-Schur Katalan functions \widetilde{\mathfrak{g}}^(k)_λ, have a product which matches the image of Monk's rule for quantum Grothendieck polynomials, established by Lenart and Maeno in 2006, under the Peterson isomorphism. We present a combinatorial method dictated by chains in the quantum Bruhat order for rewriting the product in question; the expansion relies on covers, an operation introduced by Blasiak, Morse, Pun, and Summers in 2018, novel straightening laws for generic K-theoretic Catalan functions, and a multiplication rule established by Seelinger in his PhD thesis.

This is joint with Jennifer Morse.