Toshiki Nakashima

collaborators

4 papers

math.RT2025

Characterization of the unit object in localized quantum unipotent category

Koh Matsuura, Toshiki Nakashima

For the quiver Hecke algebra $R$ , let $R -gmod$ be the category of finite-dimensional graded $R$ -modules, and let $R -gmod [w]$ be the localization of $R\hbo…

math.RT2025

Crystal Structure of Localized Quantum Unipotent Coordinate Category

Masaki Kashiwara, Toshiki Nakashima

A localized quantum unipotent coordinate category $C_{w}$ associated with a Weyl group element $w$ is a rigid monoidal category which is obtained by applying th…

math.RT2025

Decomposition Theorem for Product of Fundamental Crystals in Monomial Realization of type $C_{n}$

Manal Alshuqayr, Toshiki Nakashima

We consider a product of fundamental crystals of type $C_{n}$ in monomial realization, where the product means a natural product of Laurent monomials, not a tensor product. Then we s…

math.RT2025

Products of Kirillov-Reshetikhin modules and maximal green sequences

Yuki Kanakubo, Gleb Koshevoy, Toshiki Nakashima

We show that a $q$ -character of a Kirillov-Reshetikhin module (KR modules) for untwisted quantum affine algebras of simply laced types $A_{n}^{(1)}$ , $D_{n}^{(1)}$ , $E_{6}^{(1)}$ , $E_7^{…

Characterization of the unit object in localized quantum unipotent category

Crystal Structure of Localized Quantum Unipotent Coordinate Category

Decomposition Theorem for Product of Fundamental Crystals in Monomial Realization of type Cn​

Products of Kirillov-Reshetikhin modules and maximal green sequences

Decomposition Theorem for Product of Fundamental Crystals in Monomial Realization of type $C_{n}$