5 papers
Minuscule Relations in Quantum -Theory of Flag Varieties
Koushik Brahma, Yicen Huang, Takeshi Ikeda +2
We study the quantum -theory of the flag variety . For each minuscule fundamental weight , we construct an explicit relation in the torus-equivariant quantum -th…
Relativistic Toda lattice of type B and quantum -theory of type C flag variety
Takeshi Ikeda, Shinsuke Iwao, Takafumi Kouno +2
We introduce a classical integrable system associated with the torus-equivariant quantum -theory of type C flag variety. We prove that its conserved quantities coincide with the…
Relativistic Toda Lattice and Equivariant -Homology of Affine Grassmannian
Takeshi Ikeda, Shinsuke Iwao, Satoshi Naito +1
We investigate the phenomenon known as ''quantum equals affine'' in the setting of -equivariant quantum -theory of the flag variety , as established by Kato for any semi…
Equivariant -homology of affine Grassmannian and -theoretic double -Schur functions
Takeshi Ikeda, Mark Shimozono, Kohei Yamaguchi
We study the torus equivariant K-homology ring of the affine Grassmannian where is a connected reductive linear algebraic group. In type , we introduce equiv…
Quantum -theory of Lagrangian Grassmannian via parabolic Peterson isomorphism
Takeshi Ikeda, Takafumi Kouno, Yusuke Nakayama +1
We study Schubert calculus in the torus-equivariant quantum -ring of the Lagrangian Grassmannian . Our main tool is the -theoretic Peterson map due to Kato. T…