Séminaire Lotharingien de Combinatoire, 85B.22 (2021), 12 pp.

Cristian Lenart, Satoshi Naito and Daisuke Sagaki

A Combinatorial Chevalley Formula for Semi-Infinite Flag Manifolds and its Applications

Abstract. We give a combinatorial Chevalley formula for an arbitrary weight, in the torus-equivariant K-group of semi-infinite flag manifolds, which is expressed in terms of the quantum alcove model. As an application, we prove the Chevalley formula for anti-dominant fundamental weights in the (small) torus-equivariant quantum K-theory QK_T(G/B) of the flag manifold G/B; this has been a longstanding conjecture. We also discuss the Chevalley formula for partial flag manifolds G/P. Moreover, in type A_n-1, we prove that the so-called quantum Grothendieck polynomials indeed represent Schubert classes in the (non-equivariant) quantum K-theory QK(SL_n/B).

Received: December 1, 2020. Accepted: March 1, 2021. Final version: April 29, 2021.

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