2019/06/21 by Kato, Syu · 3 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1906.09343
We show that the equivariant small quantum K-group of a partial flag manifold is a quotient of that of the full flag manifold in a way it respects the Schubert basis. This is a K-theoretic analogue of the parabolic version of Peterson's theorem [Lam-Shimozono, Acta Math. \bf 204 (2010)] that exhibits different shape from the case of quantum cohomology. Our quotient maps send some of the Novikov variables to 1, and its geometric meaning is unclear in quantum K-theory. This paper can be seen as a continuation of [K, Ann. of Math. (to appear), and Forum of Math., Pi \bf 9 (2021)].