M. Shimozono

collaborators

4 papers

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.QA2025

Wreath Macdonald operators

Daniel Orr, Mark Shimozono, Joshua Jeishing Wen

We construct a novel family of difference-permutation operators and prove that they are diagonalized by the wreath Macdonald $P$ -polynomials; the eigenvalues are written in terms o…

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.CO2024

Marked Bumpless Pipedreams and Compatible Pairs

Daoji Huang, Mark Shimozono, Tianyi Yu

We construct a bijection between marked bumpless pipedreams with reverse compatible pairs, which are in bijection with not-necessarily-reduced pipedreams. This directly unifies var…

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

Wreath Macdonald operators

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

Marked Bumpless Pipedreams and Compatible Pairs

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

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