2020/03/31 by Takafumi Kouno, Kouno, Takafumi, Satoshi Naito +3 · 1 citation
Mathematics · #14M15 #33D52 #81R10 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Primary 17B37 #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Secondary 14N15
paper · pdf · doi:10.48550/arxiv.2003.14130
openalex publication_date 2020/03/31 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
In this paper, we give an explicit formula of Chevalley type, in terms of the Bruhat graph, for the quantum multiplication with the class of the line bundle associated to the anti-dominant minuscule fundamental weight - \varpik in the torus-equivariant quantum K-group of the partial flag manifold G/PJ (where J = I ∖ \k\) corresponding to the maximal (standard) parabolic subgroup PJ of minuscule type in type A, D, E, or B. This result is obtained by proving a similar formula in a torus-equivariant K-group of the semi-infinite partial flag manifold QJ of minuscule type, and then by making use of the isomorphism between the torus-equivariant quantum K-group of G/PJ and the torus-equivariant K-group of QJ, recently established by Kato.