Inverse $K$-Chevalley formulas for semi-infinite flag manifolds, II: arbitrary weights in ADE type

TL;DR

This paper extends inverse Chevalley formulas for the equivariant K-group of semi-infinite flag manifolds to arbitrary weights in all simply-laced types, using alcove paths, building on previous work.

Contribution

It generalizes inverse Chevalley formulas to all simply-laced types and arbitrary weights, expanding the combinatorial framework for semi-infinite flag manifolds.

Findings

Extended inverse Chevalley formulas to all simply-laced types.

Reformulated formulas using alcove paths.

Conjectured extension to E8 type.

Abstract

We continue the study, begun in [Kouno-Naito-Orr-Sagaki, 2021], of inverse Chevalley formulas for the equivariant $K$-group of semi-infinite flag manifolds. Using the language of alcove paths, we reformulate and extend our combinatorial inverse Chevalley formula to arbitrary weights in all simply-laced types (conjecturally also for $E_8$).