2023/02/19 by Toshiaki Maeno, Maeno, Toshiaki, Satoshi Naito +3 · 5 citations
Mathematics · #05E10 #14N35 #20C08 #Advanced Combinatorial Mathematics #Algebra over a field #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #Equivariant map #FOS: Mathematics #Flag (linear algebra) #Generalized flag variety #Geometry #Homotopy and Cohomology in Algebraic Topology #Ideal (ethics) #K-Theory and Homology (math.KT) #Law #Lie group #Mathematical analysis #Mathematics #Polynomial #Polynomial ring #Primary 14M15 #Principal ideal ring #Pure mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Ring (chemistry) #Secondary 14N15 #Simple ring #Torus #Type (biology)
paper · pdf · doi:10.48550/arxiv.2302.09485
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2023/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a presentation of the torus-equivariant quantum K-theory ring of flag manifolds of type A, as a quotient of a polynomial ring by an explicit ideal. This is the torus-equivariant version of our previous result, which gives a presentation of the non-equivariant quantum K-theory ring of flag manifolds of type A. However, the method of proof for the torus-equivariant one is completely different from that for the non-equivariant one; our proof is based on the result in the Q = 0 limit, and uses Nakayama-type arguments to upgrade it to the quantum situation. Also, in contrast to the non-equivariant case in which we used the Chevalley formula, we make use of the inverse Chevalley formula for the torus-equivariant K-group of semi-infinite flag manifolds to obtain a relation which yields our presentation.