K-analogues of Hivert's divided difference operators

Several families of polynomials of combinatorial and representation theoretic interest (notably the Schur polynomials s_λ, Demazure characters Dₐ, and Demazure atoms Aₐ) can be defined in terms of divided difference operators. Hivert (2000) defines "fundamental analogues" of these divided difference operators, and Hivert and Hicks-Niese show in arXiv:2406.02420 that the polynomials that arise from those fundamental operators in analogous ways to the three families of polynomials above are respectively the fundamental quasisymmetric functions Fₐ from (1984), the fundamental slides Fₐ of Assaf and Searles from arXiv:1603.09744, and the fundamental particles Pₐ of Searles from arXiv:1707.01172. Lascoux (2001) defines K-analogues of the divided difference operators, and in arXiv:1908.07364, Buciumas, Scrimshaw, and Weber show that the polynomials arising in corresponding ways from the K-theoretic divided difference operators are respectively the Grothendieck polynomials s̄_λ, the combinatorial Lascoux polynomials D̄ₐ from arXiv:1611.08777, and the combinatorial Lascoux atoms Āₐ from arXiv:1611.08777, as conjectured by Monical in arXiv:1611.08777. We define K-analogues of Hivert's fundamental divided difference operators and show that the polynomials arising in the corresponding ways from our new operators are respectively the multifundamentals F̄ₐ of Lam and Pylyavskyy from arXiv:0705.2189, the fundamental glides F̄ₐ from of Pechenik and Searles from arXiv:1611.02545, and the kaons P̄ₐ of Monical, Pechenik, and Searles from arXiv:1806.03802.