Yuki Kanakubo

activity

20142025

most citedCluster Variables on Certain Double Bruhat Cells of Type

(u, e)

and Monomial Realizations of Crystal Bases of Type A

9 citations · 19 across the 15 of their papers we have counts for

collaborators

16 papers

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^{…

math.QA2024

Monomial realizations and LS paths of fundamental representations for rank $2$ Kac-Moody algebras

Yuki Kanakubo

For a Kac-Moody algebra $g$ of rank $2$ and a fundamental weight $λ$ , we explicitly give an isomorphism between the set of Lakshmibai-Seshadri paths $B (λ)$ and…

math.QA2024

Polyhedral realizations for crystal bases and Young walls of classical affine types

Yuki Kanakubo

For affine Lie algebra $g$ of type $A_{n - 1}^{(1)}$ , $B_{n - 1}^{(1)}$ , $C_{n - 1}^{(1)}$ , $D_{n - 1}^{(1)}$ , $A_{2 n - 2}^{(2)}$ , $A_{2 n - 3}^{(2)}$ or $D_{n}^{(2)}$ , let $B (λ)$ an…

math.QA2022

An algorithm for Berenstein-Kazhdan decoration functions and trails for classical Lie algebras

Yuki Kanakubo, Gleb Koshevoy, Toshiki Nakashima

For a simply connected connected simple algebraic group $G$ , it is known that a variety $B_{w_{0}}^{-} := B^{-} \cap U w_{0} U$ has a geometric crystal structure with a positive stru…

math.QA2021

Polyhedral realizations for $B (\infty)$ and extended Young diagrams, Young walls of type $A_{n - 1}^{(1)}$ , $C_{n - 1}^{(1)}$ , $A_{2 n - 2}^{(2)}$ , $D_{n}^{(2)}$

Yuki Kanakubo

The crystal bases are quite useful combinatorial tools to study the representations of quantized universal enveloping algebras $U_{q} (g)$ . The polyhedral realization for $…

math.QA2021

An algorithm for Berenstein-Kazhdan decoration functions and trails for minuscule representations

Yuki Kanakubo, Gleb Koshevoy, Toshiki Nakashima

For a simply connected connected simple algebraic group $G$ , a cell $B_{w_{0}}^{-} = B^{-} \cap U w_{0} U$ is a geometric crystal with a positive structure $θ_{\textbf{i}}^-:(\mathbb…

math.QA2020

Adapted Sequences and Polyhedral Realizations of Crystal Bases for highest weight modules

Yuki Kanakubo, Toshiki Nakashima

The polyhedral realizations for crystal bases of the integrable highest weight modules of $U_{q} (g)$ have been introduced in ([T.Nakashima, J. Algebra, vol.219, no. 2, (19…

math.QA2019★ 3 cited

Half Potential on Geometric Crystals and Connectedness of Cellular Crystals

Yuki Kanakubo, Toshiki Nakashima

For any simple complex algebraic group, we define upper/lower half-decorated geometric crystals and show that their tropicalization will be upper/lower normal Kashiwara's crystals.…

math.QA2019

Adapted Sequence for Polyhedral Realization of Crystal Bases

Yuki Kanakubo, Toshiki Nakashima

The polyhedral realization of crystal base has been introduced by A.Zelevinsky and the second author([T.Nakashima, A.Zelevinsky, Adv. Math. 131, no. 1 (1997)]), which describe the…

math.QA2018★ 1 cited

Geometric crystals and Cluster ensembles in Kac-Moody setting

Yuki Kanakubo, Toshiki Nakashima

For a Kac-Moody group $G$ , double Bruhat cells $G^{u, e}$ ( $u$ is a Weyl group element) have positive geometric crystal structures. In arXiv:1210.2533, it is shown that there exist…

math.QA2017

Cluster algebras of finite type via a Coxeter element and Demazure Crystals of type A

Yuki Kanakubo, Toshiki Nakashima

Let $G$ be a simply connected simple algebraic group over $C$ , $B$ and $B_{-}$ be its two opposite Borel subgroups. For two elements $u$ , $v$ of the Weyl group $W$ , it is kn…

math.QA2017

Cluster algebras of finite type via a Coxeter element and Demazure Crystals of type B,C,D

Yuki Kanakubo

For a classical group $G$ and a Coxeter element $c$ of the Weyl group, it is known that the coordinate ring $C [G^{e, c^{2}}]$ of the double Bruhat cell $G^{e,c^2}:=B\cap B_-c…

math.QA2016★ 2 cited

Cluster Variables on Double Bruhat Cells $G^{u, e}$ of Classical Groups and Monomial Realizations of Demazure Crystals

Yuki Kanakubo, Toshiki Nakashima

Let $G$ be a simply connected simple algebraic group over $C$ , $B$ and $B_{-}$ its two opposite Borel subgroups, and $W$ the associated Weyl group. It is shown that the coor…

math.QA2016★ 1 cited

Explicit Forms of Cluster Variables on Double Bruhat Cells G^{u,e} of type B

Yuki Kanakubo

Let $G$ be a simply connected simple algebraic group over $C$ of type $B_{r}$ , $B$ and $B_{-}$ be its two opposite Borel subgroups, and $W$ be the associated Weyl group. For $…

math.QA2015★ 3 cited

Explicit Forms of Cluster Variables on Double Bruhat Cells G^{u,e} of type C

Yuki Kanakubo, Toshiki Nakashima

Let $G = S p_{2 r} (C)$ be a simply connected simple algebraic group over $C$ of type $C_{r}$ , $B$ and $B_{-}$ be its two opposite Borel subgroups, and $W$ be the associa…

math.QA2014★ 9 cited

Cluster Variables on Certain Double Bruhat Cells of Type $(u, e)$ and Monomial Realizations of Crystal Bases of Type A

Yuki Kanakubo, Toshiki Nakashima

Let $G$ be a simply connected simple algebraic group over $C$ , $B$ and $B_{-}$ be two opposite Borel subgroups in $G$ and $W$ be the Weyl group. For $u$ , $v \in W$ , it is kno…

Products of Kirillov-Reshetikhin modules and maximal green sequences

Monomial realizations and LS paths of fundamental representations for rank 2 Kac-Moody algebras

Polyhedral realizations for crystal bases and Young walls of classical affine types

An algorithm for Berenstein-Kazhdan decoration functions and trails for classical Lie algebras

Polyhedral realizations for B(∞) and extended Young diagrams, Young walls of type An−1(1)​, Cn−1(1)​, A2n−2(2)​, Dn(2)​

An algorithm for Berenstein-Kazhdan decoration functions and trails for minuscule representations

Adapted Sequences and Polyhedral Realizations of Crystal Bases for highest weight modules

Half Potential on Geometric Crystals and Connectedness of Cellular Crystals

Adapted Sequence for Polyhedral Realization of Crystal Bases

Geometric crystals and Cluster ensembles in Kac-Moody setting

Cluster algebras of finite type via a Coxeter element and Demazure Crystals of type A

Cluster algebras of finite type via a Coxeter element and Demazure Crystals of type B,C,D

Cluster Variables on Double Bruhat Cells Gu,e of Classical Groups and Monomial Realizations of Demazure Crystals

Explicit Forms of Cluster Variables on Double Bruhat Cells G^{u,e} of type B

Explicit Forms of Cluster Variables on Double Bruhat Cells G^{u,e} of type C

Cluster Variables on Certain Double Bruhat Cells of Type (u,e) and Monomial Realizations of Crystal Bases of Type A

Monomial realizations and LS paths of fundamental representations for rank $2$ Kac-Moody algebras

Polyhedral realizations for $B (\infty)$ and extended Young diagrams, Young walls of type $A_{n - 1}^{(1)}$ , $C_{n - 1}^{(1)}$ , $A_{2 n - 2}^{(2)}$ , $D_{n}^{(2)}$

Cluster Variables on Double Bruhat Cells $G^{u, e}$ of Classical Groups and Monomial Realizations of Demazure Crystals

Cluster Variables on Certain Double Bruhat Cells of Type $(u, e)$ and Monomial Realizations of Crystal Bases of Type A