カナクボ ユウキ金久保 有輝助教Kanakubo Yuki
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論文
- Monomial realizations and LS paths of fundamental representations for rank 2 Kac-Moody algebras
Yuki Kanakubo, Elsevier BV
Journal of Algebra, 2025年06月, ［査読有り］ - An Algorithm for Berenstein–Kazhdan Decoration Functions and Trails for Classical Lie Algebras
Yuki Kanakubo; Gleb Koshevoy; Toshiki Nakashima, Abstract
For a simply connected connected simple algebraic group $G$, it is known that a variety $B_{w_0}^-:=B^-\cap U\overline{w_0}U$ has a geometric crystal structure with a positive structure $\theta ^-_{\textbf{i } }:(\mathbb{C}^{\times })^{l(w_0)}\rightarrow B_{w_0}^-$ for each reduced word $\textbf{i}$ of the longest element $w_0$ of Weyl group. A rational function $\Phi ^h_{BK}=\sum _{i\in I}\Delta _{w_0\Lambda _i,s_i\Lambda _i}$ on $B_{w_0}^-$ is called a half-potential, where $\Delta _{w_0\Lambda _i,s_i\Lambda _i}$ is a generalized minor. Computing $\Phi ^h_{BK}\circ \theta ^-_{\textbf{i } }$ explicitly, we get an explicit form of string cone or polyhedral realization of $B(\infty )$ for the finite dimensional simple Lie algebra $\mathfrak{g}=\textrm{Lie}(G)$. In this paper, for an arbitrary reduced word $\textbf{i}$, we give an algorithm to compute the summand $\Delta _{w_0\Lambda _i,s_i\Lambda _i}\circ \theta ^-_{\textbf{i } }$ of $\Phi ^h_{BK}\circ \theta ^-_{\textbf{i } }$ in the case $i\in I$ satisfies that for any weight $\mu $ of $V(-w_0\Lambda _i)$ and $t\in I$, it holds $\langle h_t,\mu \rangle \in \{2,1,0,-1,-2\}$. In particular, if $\mathfrak{g}$ is of type $\textrm{A}_n$, $\textrm{B}_n$, $\textrm{C}_n$ or $\textrm{D}_n$ then all $i\in I$ satisfy this condition so that one can completely calculate $\Phi ^h_{BK}\circ \theta ^-_{\textbf{i } }$. We will also prove that our algorithm works in the case $\mathfrak{g}$ is of type $\textrm{G}_2$., Oxford University Press (OUP)
International Mathematics Research Notices, 2024年02月, ［査読有り］ - Polyhedral Realizations for $B(\infty )$ and Extended Young Diagrams, Young Walls of Type $\mathrm {A}^{(1)}_{n-1}$, $\mathrm {C}^{(1)}_{n-1}$, $\mathrm {A}^{(2)}_{2n-2}$, $\mathrm {D}^{(2)}_{n}$
Yuki Kanakubo, Springer Science and Business Media LLC
Algebras and Representation Theory, 2023年10月, ［査読有り］ - Polyhedral realizations for crystal bases of integrable highest weight modules and combinatorial objects of type $\mathrm {A}^{(1)}_{n-1}$, $\mathrm {C}^{(1)}_{n-1}$, $\mathrm {A}^{(2)}_{2n-2}$, $\mathrm {D}^{(2)}_{n}$
金久保 有輝, Springer Science and Business Media LLC
Letters in Mathematical Physics, 2023年05月28日, ［査読有り］ - HALF POTENTIAL ON GEOMETRIC CRYSTALS AND CONNECTEDNESS OF CELLULAR CRYSTALS
YUKI KANAKUBO; TOSHIKI NAKASHIMA, Springer Science and Business Media LLC
Transformation Groups, 2023年03月, ［査読有り］ - An algorithm for Berenstein-Kazhdan decoration functions and trails for minuscule representations
Yuki Kanakubo; Gleb Koshevoy; Toshiki Nakashima, Elsevier BV
Journal of Algebra, 2022年10月, ［査読有り］ - Adapted sequences and polyhedral realizations of crystal bases for highest weight modules
Yuki Kanakubo; Toshiki Nakashima, Elsevier BV
Journal of Algebra, 2021年05月, ［査読有り］ - Adapted sequence for polyhedral realization of crystal bases
Yuki Kanakubo; Toshiki Nakashima, Informa UK Limited
Communications in Algebra, 2020年11月, ［査読有り］ - Geometric crystals and cluster ensembles in Kac-Moody setting
Yuki Kanakubo; Toshiki Nakashima
Journal of Geometry and Physics, 2020年03月, ［査読有り］ - Cluster algebras of finite type via Coxeter elements and Demazure Crystals of type A
Yuki Kanakubo; Toshiki Nakashima
Journal of Algebra, 2019年11月, ［査読有り］ - Cluster algebras of finite type via Coxeter elements and Demazure Crystals of type B,C,D
Yuki Kanakubo
Journal of Geometry and Physics, 2019年03月, ［査読有り］ - Cluster Variables on Double Bruhat Cells G^{u,e} of Classical Groups and Monomial Realizations of Demazure Crystals
Yuki Kanakubo; Toshiki Nakashima
International Mathematics Research Notices, 2018年06月, ［査読有り］ - Explicit Forms of Cluster Variables on Double Bruhat Cells of Type C
Yuki Kanakubo; Toshiki Nakashima, Let G = Sp2r(C) be a simply connected simple algebraic group over C of type Cr, B and B_ its two opposite Borel subgroups, and W the associated Weyl group. For u, v is an element of W, it is known that the coordinate ring C[G(u,v)] of the double Bruhat cell G(u,v) = BuB U B_vB_ is isomorphic to an upper cluster algebra (A) over bar (i)c and the generalized minors Delta(k; i) are the cluster variables of C[G(u,v)][5]. In the case v = e, we shall describe the generalized minor Delta(k; i) explicitly., TOKYO JOURNAL MATHEMATICS EDITORIAL OFFICE ACAD CENTER
TOKYO JOURNAL OF MATHEMATICS, 2017年03月, ［査読有り］ - 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 u, vW, it is known that the coordinate ring C[G(u,v)] of the double Bruhat cell G(u,v) = BuB boolean OR B(-)vB(-) is isomorphic to an upper cluster algebra (A) over bar (i)(C) and generalized minors Delta(k; i) are the cluster variables of C[G(u,v)][1]. It is also shown that C[G(u,v)] have a structure of cluster algebra [6]. In the case v = e, we shall describe the generalized minor Delta(k; i) explicitly., TAYLOR & FRANCIS INC
COMMUNICATIONS IN ALGEBRA, 2017年03月, ［査読有り］ - Cluster Variables on Certain Double Bruhat Cells of Type (u, e) and Monomial Realizations of Crystal Bases of Type A
Yuki Kanakubo; Toshi Nakashima, Let C be a simply connected simple algebraic group over C, B and B_ be two opposite Borel subgroups in C and W be the Weyl group. For u, v is an element of W, it is known that the coordinate ring C[C-u,C- v] of the double Bruhat cell C-u,C- v = BuB boolean AND B_vB_ is isomorphic to an upper cluster algebra (A) over bar( i)(C) and the generalized minors {Delta(k; i)} are the cluster variables belonging to a given initial seed in C[C-u,C- v] [Berenstein A., Fomin S., Zelevinsky A., Duke Math. J. 126 (2005), 1-52]. In the case C = SLr+1 (C), v = e and some special u is an element of W, we shall describe the generalized minors {Delta(k; i)} as summations of monomial realizations of certain Demazure crystals., NATL ACAD SCI UKRAINE, INST MATH
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 2015年04月, ［査読有り］
MISC
講演・口頭発表等
- Inequalities defining polyhedral realizations and monomial realizations of crystal bases
Yuki Kanakubo
Combinatorics and Arithmetic for Physics : special days, 2024年11月22日, ［招待有り］
20241120, 20241122 - Polyhedral realizations and Young walls of classical affine types
金久保 有輝
"Crystal Bases and Then..." - Conference in honor of Toshiki Nakashima's 60th birthday -, 2024年07月12日, ［招待有り］
20240709, 20240712 - An algorithm for Berenstein-Kazhdan decoration functions on classical groups
Yuki Kanakubo
Cologne Algebra and Representation Theory Seminar, 2023年12月12日, ［招待有り］
20231212, 20231212 - Polyhedral realizations for crystal bases and extended Young diagrams of affine type A^{(1)}_{n-1}
金久保 有輝
MPI-Oberseminar, 2023年11月23日
20231123, 20231123 - Inequalities defining polyhedral realizations of affine types and extended Young diagrams
金久保 有輝
Combinatorics and Arithmetic for Physics: special days, Tenth Anniversary Edition, 2023年11月17日, ［招待有り］
20231115, 20231117 - Polyhedral realizations and extended Young diagrams of several classical affine types
金久保 有輝
上智大学数学談話会, 2023年07月21日, ［招待有り］ - An algorithm for Berenstein-Kazhdan decoration functions on classical groups
金久保 有輝
東工大表現論セミナー, 2023年07月14日, ［招待有り］ - Polyhedral realizations and extended Young diagrams of several classical affine types
金久保 有輝
物理的な代数と組合せ数学セミナー, 2023年03月24日, ［招待有り］ - An algorithm for Berenstein-Kazhdan decoration functions on classical groups
金久保 有輝
Algebraic Lie Theory and Representation Theory (ALTReT) 2022, 2022年05月26日
20220523, 20220527 - An algorithm for Berenstein-Kazhdan decoration functions for minuscule representations
金久保有輝
日本数学会2022年度年会, 2022年03月30日
20220328, 20220331 - Polyhedral realizations and extended Young diagrams, Young walls of several classical affine types
金久保有輝
RIMS共同研究「組合せ論的表現論および関連分野との連携」, 2021年10月20日
20211018, 20211022 - The inequalities defining polyhedral realizations and monomial realizations of crystal bases
金久保 有輝
組合せ論的表現論の最近の進展, 2020年10月08日, ［招待有り］
20201005, 20201008 - Adapted Sequence for Polyhedral Realization of Crystal Bases
金久保 有輝
The 2nd Meeting for Study of Number theory, Hopf algebras and related topics, 2020年02月16日, ［招待有り］
20200215, 20200218 - Adapted Sequence for Polyhedral Realization of Crystal Bases
金久保 有輝
表現論とその組合せ論的側面, 2019年10月28日
20191028, 20191031 - Cluster theory on double Bruhat cells and crystal bases
Yuki Kanakubo
Cluster Algebras 2019, 2019年06月14日, ［招待有り］ - Adapted Sequence for Polyhedral Realization of Crystal Bases
Yuki Kanakubo
Algebraic Lie Theory and Representation Theory 2019, 2019年05月 - Positivity condition of Polyhedral realizations of crystal bases
Yuki Kanakubo
Crystals and Their Generalizations, 2019年03月26日, ［招待有り］ - Positivity condition of Polyhedral realizations of crystal bases
Yuki Kanakubo
Meeting of crystal basis and quantum algebras and superalgebras, 2018年11月14日, ［招待有り］ - Cluster algebra structures of the coordinate rings and crystal bases
Yuki Kanakubo
岡山理科大学,『第8回 半田山・幾何・代数セミナー』, 2018年01月11日, ［招待有り］ - Cluster algebras of finite type and crystal bases
Yuki Kanakubo
Infinite Analysis 17, Algebraic and Combinatorial Aspects in Integrable Systems, 2017年12月06日, ［招待有り］ - Cluster algebras of finite type via a Coxeter element and Demazure Crystals
Yuki Kanakubo
Algebraic Analysis and Representation Theory, 2017年06月 - Cluster variables on double Bruhat cells of classical groups and crystal bases
Yuki Kanakubo
筑波大学数学特別セミナー, 2016年11月04日, ［招待有り］ - Finite type cluster algebras and Demazure crystals
Yuki Kanakubo
RIMS 研究集会「リー型の組合せ論」, 2016年10月05日 - Cluster variables on double Bruhat cells of classical groups and crystal bases
Yuki Kanakubo
第2回 Algebraic Lie Theory and Representation Theory, 2016年06月 - 古典群のdouble Bruhat cell上のクラスター変数と結晶基底
金久保有輝
日本数学会2016年度年会, 2016年03月 - 古典群のdouble Bruhat cell 上のクラスター変数と結晶基底
Yuki Kanakubo
第12回 数学総合若手研究集会, 2016年03月 - 結晶基底と，Double Bruhat cell 上の座標環のクラスター変数
Yuki Kanakubo
上智大学 数学談話会, 2015年07月, ［招待有り］ - Cluster Variables on Double Bruhat Cells and Monomial Realizations of Crystal Bases
金久保有輝
日本数学会 2014年度秋季総合分科会, 2014年09月 - Cluster Variables on Double Bruhat Cells and Monomial Realizations of Crystal Bases
Yuki Kanakubo
RIMS 研究集会「表現論と調和解析の新たな進展」, 2014年06月 - Cluster Variables on Double Bruhat Cells and Monomial Realizations of Crystal Bases
Yuki Kanakubo
第17回代数群と量子群の表現論, 2014年06月
担当経験のある科目（授業）
共同研究・競争的資金等の研究課題
