Takeshi Ikeda

activity

20242026

collaborators

8 papers

math.RT2026

Minuscule Relations in Quantum $K$ -Theory of Flag Varieties

Koushik Brahma, Yicen Huang, Takeshi Ikeda +2

We study the quantum $K$ -theory of the flag variety $G / B$ . For each minuscule fundamental weight $ϖ$ , we construct an explicit relation in the torus-equivariant quantum $K$ -th…

math.RT2026

Relativistic Toda lattice of type B and quantum $K$ -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 $K$ -theory of type C flag variety. We prove that its conserved quantities coincide with the…

math.CO2026

Neutral-Fermion constructions of factorial $g p$ -and $g q$ -Functions

Koushik Brahma, Takeshi Ikeda, Shinsuke Iwao +1

We develop neutral-fermionic constructions for the factorial $g p$ -and $g q$ -functions introduced by Nakagawa and Naruse, which are respectively dual to the factorial $GQ$ - and $GP$ -…

math.AG2026

Seidel product formula in equivariant quantum $K$ -theory of flag varieties

Takeshi Ikeda, Takafumi Kouno, Satoshi Naito

We prove a Seidel product formula for the torus-equivariant quantum $K$ -theory of a generalized flag variety $G / P .$ This is a natural generalization of the corresponding results by…

math.RT2025

Equivariant homology of the symplectic affine Grassmannian and dual affine Schur $P$ -functions

Takeshi Ikeda, Shinsuke Iwao, Mark Shimozono

We study the torus-equivariant homology $H_{*}^{T} (Gr_{G})$ of the affine Grassmannian $Gr_{G}$ , where $G = Sp_{2 n} (C)$ is the symplectic group. This homo…

math.RT2025

Relativistic Toda Lattice and Equivariant $K$ -Homology of Affine Grassmannian

Takeshi Ikeda, Shinsuke Iwao, Satoshi Naito +1

We investigate the phenomenon known as ''quantum equals affine'' in the setting of $T$ -equivariant quantum $K$ -theory of the flag variety $G / B$ , as established by Kato for any semi…

math.RT2024

Equivariant $K$ -homology of affine Grassmannian and $K$ -theoretic double $k$ -Schur functions

Takeshi Ikeda, Mark Shimozono, Kohei Yamaguchi

We study the torus equivariant K-homology ring of the affine Grassmannian $Gr_{G}$ where $G$ is a connected reductive linear algebraic group. In type $A$ , we introduce equiv…

math.AG2024

Quantum $K$ -theory of Lagrangian Grassmannian via parabolic Peterson isomorphism

Takeshi Ikeda, Takafumi Kouno, Yusuke Nakayama +1

We study Schubert calculus in the torus-equivariant quantum $K$ -ring of the Lagrangian Grassmannian $LG (n)$ . Our main tool is the $K$ -theoretic Peterson map due to Kato. T…

Minuscule Relations in Quantum K-Theory of Flag Varieties

Relativistic Toda lattice of type B and quantum K-theory of type C flag variety

Neutral-Fermion constructions of factorial gp-and gq-Functions

Seidel product formula in equivariant quantum K-theory of flag varieties

Equivariant homology of the symplectic affine Grassmannian and dual affine Schur P-functions

Relativistic Toda Lattice and Equivariant K-Homology of Affine Grassmannian

Equivariant K-homology of affine Grassmannian and K-theoretic double k-Schur functions

Quantum K-theory of Lagrangian Grassmannian via parabolic Peterson isomorphism