Kanakubo YukiAssistant Professor
■Researcher basic information
Organization
Career
- Apr. 2024 - Present, Ibaraki University
- Sep. 2023 - Mar. 2024, Max Planck Institute for Mathematics, Postdoctoral Research Fellow
- Sep. 2020 - Aug. 2023, University of Tsukuba, School of Science and Engineering, 非常勤講師
- Apr. 2020 - Mar. 2023, University of Tsukuba, 日本学術振興会 特別研究員 PD
- Apr. 2017 - Mar. 2020, Sophia University, 理工学部, 特別研究員(PD)
External link
■Research activity information
Paper
- Monomial realizations and LS paths of fundamental representations for rank 2 Kac-Moody algebras
Yuki Kanakubo, Elsevier BV
Journal of Algebra, Jun. 2025, [Reviewed] - 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, Feb. 2024, [Reviewed] - 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, Oct. 2023, [Reviewed] - Polyhedral realizations for crystal bases of integrable highest weight modules and combinatorial objects of type $\mathrm {A}^{(1)}_{n-1}$, $\mathrm {C}^{(1)}_{n-1}$, $\mathrm {A}^{(2)}_{2n-2}$, $\mathrm {D}^{(2)}_{n}$
Yuki Kanakubo, Springer Science and Business Media LLC
Letters in Mathematical Physics, 28 May 2023, [Reviewed] - HALF POTENTIAL ON GEOMETRIC CRYSTALS AND CONNECTEDNESS OF CELLULAR CRYSTALS
YUKI KANAKUBO; TOSHIKI NAKASHIMA, Springer Science and Business Media LLC
Transformation Groups, Mar. 2023, [Reviewed] - An algorithm for Berenstein-Kazhdan decoration functions and trails for minuscule representations
Yuki Kanakubo; Gleb Koshevoy; Toshiki Nakashima, Elsevier BV
Journal of Algebra, Oct. 2022, [Reviewed] - Adapted sequences and polyhedral realizations of crystal bases for highest weight modules
Yuki Kanakubo; Toshiki Nakashima, Elsevier BV
Journal of Algebra, May 2021, [Reviewed] - Adapted sequence for polyhedral realization of crystal bases
Yuki Kanakubo; Toshiki Nakashima, Informa UK Limited
Communications in Algebra, Nov. 2020, [Reviewed] - Geometric crystals and cluster ensembles in Kac-Moody setting
Yuki Kanakubo; Toshiki Nakashima
Journal of Geometry and Physics, Mar. 2020, [Reviewed] - Cluster algebras of finite type via Coxeter elements and Demazure Crystals of type A
Yuki Kanakubo; Toshiki Nakashima
Journal of Algebra, Nov. 2019, [Reviewed] - Cluster algebras of finite type via Coxeter elements and Demazure Crystals of type B,C,D
Yuki Kanakubo
Journal of Geometry and Physics, Mar. 2019, [Reviewed] - 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, Jun. 2018, [Reviewed] - Explicit Forms of Cluster Variables on Double Bruhat Cells of Type C
Yuki Kanakubo; Toshiki Nakashima
TOKYO JOURNAL OF MATHEMATICS, Mar. 2017, [Reviewed] - Explicit forms of cluster variables on double Bruhat cells G^{u,e} of type B
Yuki Kanakubo
COMMUNICATIONS IN ALGEBRA, Mar. 2017, [Reviewed] - Cluster Variables on Certain Double Bruhat Cells of Type (u, e) and Monomial Realizations of Crystal Bases of Type A
Yuki Kanakubo; Toshi Nakashima
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, Apr. 2015, [Reviewed]
MISC
- Explicit forms of polyhedral realizations of crystal bases associated with adapted sequences
Yuki Kanakubo; Toshiki Nakashima
Toyama Mathematical Journal, 2021, [Reviewed] - Cluster Variables on Double Bruhat Cells and Monomial Realizations of Crystal Bases (New Developments of Representation Theory and Harmonic Analysis)
Kanakubo Yuki
RIMS Kokyuroku, Nov. 2014
Lectures, oral presentations, etc.
- A conjecture on inequalities defining polyhedral realizations and monomial realizations of crystal bases
Yuki Kanakubo
SNU department seminar, 06 Feb. 2026, [Invited] - Inequalities defining polyhedral realizations and monomial realizations of crystal bases
Yuki Kanakubo
Confluence of combinatorics and representation theory, 22 Oct. 2025
20251021, 20251024 - Inequalities defining polyhedral realizations and monomial realizations of crystal bases
Yuki Kanakubo
Combinatorics and Arithmetic for Physics : special days, 22 Nov. 2024, [Invited]
20241120, 20241122 - Polyhedral realizations and Young walls of classical affine types
Yuki Kanakubo
"Crystal Bases and Then..." - Conference in honor of Toshiki Nakashima's 60th birthday -, 12 Jul. 2024, [Invited]
20240709, 20240712 - An algorithm for Berenstein-Kazhdan decoration functions on classical groups
Yuki Kanakubo
Cologne Algebra and Representation Theory Seminar, 12 Dec. 2023, [Invited]
20231212, 20231212 - Polyhedral realizations for crystal bases and extended Young diagrams of affine type A^{(1)}_{n-1}
Yuki Kanakubo
MPI-Oberseminar, 23 Nov. 2023
20231123, 20231123 - Inequalities defining polyhedral realizations of affine types and extended Young diagrams
Yuki Kanakubo
Combinatorics and Arithmetic for Physics: special days, Tenth Anniversary Edition, 17 Nov. 2023, [Invited]
20231115, 20231117 - Polyhedral realizations and extended Young diagrams of several classical affine types
Yuki Kanakubo
Sophia University Mathematics Colloquium, 21 Jul. 2023, [Invited] - An algorithm for Berenstein-Kazhdan decoration functions on classical groups
Yuki Kanakubo
Tokyo Tech Representation Theory Seminar, 14 Jul. 2023, [Invited] - Polyhedral realizations and extended Young diagrams of several classical affine types
Yuki Kanakubo
Physical Algebra and Combinatorics Seminar, 24 Mar. 2023, [Invited] - An algorithm for Berenstein-Kazhdan decoration functions on classical groups
Yuki Kanakubo
Algebraic Lie Theory and Representation Theory (ALTReT) 2022, 26 May 2022
20220523, 20220527 - An algorithm for Berenstein-Kazhdan decoration functions for minuscule representations
Yuki Kanakubo
MSJ Spring Meeting 2022, 30 Mar. 2022
20220328, 20220331 - Polyhedral realizations and extended Young diagrams, Young walls of several classical affine types
Yuki Kanakubo
RIMS workshop, Combinatorial Representation Theory and Connections with Related Fields, 20 Oct. 2021
20211018, 20211022 - The inequalities defining polyhedral realizations and monomial realizations of crystal bases
Yuki Kanakubo
組合せ論的表現論の最近の進展, 08 Oct. 2020, [Invited]
20201005, 20201008 - Adapted Sequence for Polyhedral Realization of Crystal Bases
Yuki Kanakubo
The 2nd Meeting for Study of Number theory, Hopf algebras and related topics, 16 Feb. 2020, [Invited]
20200215, 20200218 - Adapted Sequence for Polyhedral Realization of Crystal Bases
Yuki Kanakubo
Representation Theory and its Combinatorial Aspects, 28 Oct. 2019
20191028, 20191031 - Cluster theory on double Bruhat cells and crystal bases
Yuki Kanakubo
Cluster Algebras 2019, 14 Jun. 2019, [Invited] - Adapted Sequence for Polyhedral Realization of Crystal Bases
Yuki Kanakubo
Algebraic Lie Theory and Representation Theory 2019, May 2019 - Positivity condition of Polyhedral realizations of crystal bases
Yuki Kanakubo
Crystals and Their Generalizations, 26 Mar. 2019, [Invited] - Positivity condition of Polyhedral realizations of crystal bases
Yuki Kanakubo
Meeting of crystal basis and quantum algebras and superalgebras, 14 Nov. 2018, [Invited] - Cluster algebra structures of the coordinate rings and crystal bases
Yuki Kanakubo
Okayama University of Science, 『第8回 半田山・幾何・代数セミナー』, 11 Jan. 2018, [Invited] - Cluster algebras of finite type and crystal bases
Yuki Kanakubo
Infinite Analysis 17, Algebraic and Combinatorial Aspects in Integrable Systems, 06 Dec. 2017, [Invited] - Cluster algebras of finite type via a Coxeter element and Demazure Crystals
Yuki Kanakubo
Algebraic Analysis and Representation Theory, Jun. 2017 - 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, 04 Nov. 2016, [Invited] - Finite type cluster algebras and Demazure crystals
Yuki Kanakubo
RIMS 研究集会「リー型の組合せ論」, 05 Oct. 2016 - Cluster variables on double Bruhat cells of classical groups and crystal bases
Yuki Kanakubo
第2回 Algebraic Lie Theory and Representation Theory, Jun. 2016 - Cluster variables on double Bruhat cells of classical groups and crystal bases
Yuki Kanakubo
MSJ Spring Meeting 2016, Mar. 2016 - 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, Mar. 2016 - 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, Jul. 2015, [Invited] - Cluster Variables on Double Bruhat Cells and Monomial Realizations of Crystal Bases
Yuki Kanakubo
MSJ Autumn Meeting 2014, Sep. 2014 - 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」, Jun. 2014 - 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, Jun. 2014
Courses
- Exercise in Linear algebra S
May 2023 - Aug. 2023
University of Tsukuba - Math literacy 2
Jun. 2022 - Jul. 2022
University of Tsukuba - Math literacy 1
Apr. 2022 - May 2022
University of Tsukuba - Exercise in linear algebra F
Nov. 2021 - Feb. 2022
University of Tsukuba - Math literacy 2
Jun. 2021 - Jul. 2021
University of Tsukuba - Math literacy 1
Apr. 2021 - May 2021
University of Tsukuba - Exercise in linear algebra F
Nov. 2020 - Feb. 2021
University of Tsukuba - Linear algebra I
Sep. 2020 - Sep. 2020
University of Tsukuba - Calculus I
Sep. 2020 - Sep. 2020
University of Tsukuba
Research Themes
- Polyhedral realizations for Verma modules and extremal weight modules and star crystal structures
Grant in Aid for Scientific Research (C) (General)
Ibaraki university
Apr. 2026 - Mar. 2029 - Characterization of polyhedral realizations for crystal bases and applications for cluster theory
Grant-in-Aid for Research Activity Start-up
Ibaraki university
Jul. 2024 - Mar. 2026 - Combinatorial descriptions of crystal bases and applications to the cluster theory
Grant-in-Aid for JSPS Fellows
University of Tsukuba
Apr. 2020 - Mar. 2023 - Relations between cluster algebras and crystal bases, geometric crystals
Grant-in-Aid for Research Activity Start-up
Sophia University
Aug. 2017 - Mar. 2019
