8 papers
Borel-type presentation of the torus-equivariant quantum -ring of flag manifolds of type
Takafumi Kouno, Satoshi Naito
We give a Borel-type presentation of the torus-equivariant (small) quantum -ring of flag manifolds of type .
A generalization of quantum Lakshmibai-Seshadri paths for arbitrary weights
Takafumi Kouno, Satoshi Naito
We construct an injective weight-preserving map (called the forgetful map) from the set of all admissible subsets in the quantum alcove model associated to an arbitrary weight. The…
Identities of inverse Chevalley type for graded characters of level-zero Demazure submodules over quantum affine algebras of type C
Takafumi Kouno, Satoshi Naito, Daniel Orr
We provide identities of inverse Chevalley type for the graded characters of level-zero Demazure submodules of extremal weight modules over a quantum affine algebra of type . Th…
Quantum K-theory Chevalley formulas in the parabolic case
Takafumi Kouno, Cristian Lenart, Satoshi Naito +3
We derive cancellation-free Chevalley-type multiplication formulas in the T-equivariant quantum K-theory of Grassmannians of type A and C, and also those of two-step flag manifolds…
New structure on the quantum alcove model with applications to representation theory and Schubert calculus
Takafumi Kouno, Cristian Lenart, Satoshi Naito
The quantum alcove model associated to a dominant weight plays an important role in many branches of mathematics, such as combinatorial representation theory, the theory of Macdona…
Inverse -Chevalley formulas for semi-infinite flag manifolds, I: minuscule weights in ADE type
Takafumi Kouno, Satoshi Naito, Daniel Orr +1
We prove an explicit inverse Chevalley formula in the equivariant -theory of semi-infinite flag manifolds of simply-laced type. By an inverse Chevalley formula, we mean a formul…