Séminaire Lotharingien de Combinatoire, 86B.13 (2022), 12 pp.

Takafumi Kouno, Cristian Lenart and Satoshi Naito

Generalized Quantum Yang-Baxter Moves and Their Application to Schubert Calculus

Abstract. The quantum alcove model is a uniform combinatorial model in the representation theory of quantum affine algebras and Schubert calculus on flag manifolds. Given a weight λ, the model is based on a sequence of roots called a λ-chain. When λ is dominant, the independence of the model from the chosen λ-chain was shown using certain elementary transformations called quantum Yang-Baxter moves. The purpose of the present work is to generalize the quantum Yang-Baxter moves to an arbitrary weight λ. As an application, we give a combinatorial proof of the Chevalley formula in the equivariant K-group of semi-infinite flag manifolds, first proved by Lenart-Naito-Sagaki.

Received: November 25, 2021. Accepted: March 4, 2022. Final version: April 1, 2022.

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