Inverse K Chevalley formulas for semi in

This paper continues the exploration of inverse Chevalley formulas for the equivariant K-group of semi-infinite flag manifolds, extending previous work on the subject. The main objective is to generalize the combinatorial inverse Chevalley formula to accommodate arbitrary weights in simply-laced types, following the initial findings documented in a prior study. Utilizing the language of alcove paths, the methodology involves reformulating the established combinatorial framework to develop a new formula that addresses the complexities arising from non-dominant weights. The results indicate a successful extension of the inverse Chevalley formula, illustrating that it can be effectively articulated through the lens of alcove paths, thereby reinforcing the alignment with existing combinatorial results and providing deeper insights into the structure of the equivariant K-group. The paper argues that this advancement not only broadens the applicability of the inverse Chevalley formula but also contributes to the overarching understanding of algebraic groups and their K-theoretic properties.