Shaplin III, Richard Martin2024-05-082024-05-082024-05-07vt_gsexam:40590https://hdl.handle.net/10919/118915The inverse Chevalley formula in the equivariant K-theory of semi-infinite flag manifolds of type An−1 is given as a sum over a set of quantum walks in the quantum Bruhat graph, QBG(An−1). We establish bounds on the number of quantum steps and simple stationary steps in these quantum walks. By a result of Kato, we map this formula to the equivariant quantum K-theory of partial flag manifolds G/P to give an alternate proof of [KLNS24, Theorem 8].ETDenCreative Commons Attribution 4.0 InternationalQuantum WalksK-TheoryDissertation