7 papers
On quantum -groups of partial flag manifolds
Syu Kato
We show that the equivariant small quantum -group of a partial flag manifold is a quotient of that of the full flag manifold in a way that respects the Schubert classes. This is…
A geometric realization of Catalan functions
Syu Kato
We construct a smooth projective variety that compactifies an equivariant vector subbundle of the cotangent bundle of the flag variety for , determi…
Categorification of -Schur functions and refined Macdonald positivity
Syu Kato
We characterize the -Schur functions as the graded characters of simple objects in an additive module category. This confirms a set of conjectures formulated in the Ph.D. thesis…
Higher level BGG reciprocity for current algebras
Syu Kato
We exhibit a higher-level analogue of the Bernstein-Gelfand-Gelfand (BGG) reciprocity for twisted current algebras for each positive integer, which recovers the original one (estab…
Loop structure on equivariant -theory of semi-infinite flag manifolds
Syu Kato
We explain that the Pontryagin product structure on the equivariant -group of an affine Grassmannian considered in [Lam-Schilling-Shimozono, Compos. Math. {\bf 146} (2010)] coin…
A geometric realization of the chromatic symmetric function of a unit interval graph
Syu Kato
Shareshian-Wachs, Brosnan-Chow, and Guay-Pacquet [Adv. Math. (2016), (2018), arXiv:1601.05498] realized the chromatic (quasi-)symmetric function of a unit i…