Updated on 2022/05/25

写真a

 
IKEDA, Takeshi
 
Affiliation
Faculty of Science and Engineering, School of Fundamental Science and Engineering
Job title
Professor
Profile
群作用を持つ代数多様体の性質を組合せ論的な方法によって研究している．特に，グラスマン多様体などの一般旗多様体におけるシューベルト部分多様体の（一般化された）コホモロジー類を扱う．コホモロジー類を代表する特殊多項式の理論を整備・展開すること，およびその応用を主に目指している．関連が深い分野である可積分系や表現論の考え方も取り入れて研究を行っている．

Concurrent Post

  • Faculty of Science and Engineering   Graduate School of Fundamental Science and Engineering

Research Institute

  • 2020
    -
    2022

    理工学術院総合研究所   兼任研究員

Education

  • 1993.04
    -
    1996.03

    東北大学大学院   理学研究科   数学専攻 博士課程後期3年の課程  

  • 　
    -
    1996

    Tohoku University   Graduate School, Division of Natural Science  

  • 1991.04
    -
    1993.03

    東北大学大学院   理学研究科   数学専攻 博士課程前期2年の課程  

  • 1987.04
    -
    1991.03

    Tohoku University   Faculty of Science   Department of Physics  

  • 　
    -
    1991

    Tohoku University   Faculty of Science  

Degree

  • (BLANK)

  • (BLANK)

Research Experience

  • 1998.04
    -
    Now

    Okayama University of Science   Faculty of Science, Department of Applied Mathematics

Professional Memberships

  • 　
    　
    　

    日本数学会

 

Research Areas

  • Algebra

Research Interests

  • combinatorics

  • integrable systems

  • representation theory

  • algebraic geometry

Papers

  • FACTORIAL P- AND Q-SCHUR FUNCTIONS REPRESENT EQUIVARIANT QUANTUM SCHUBERT CLASSES

    Takeshi Ikeda, Leonardo C. Mihalcea, Hiroshi Naruse

    OSAKA JOURNAL OF MATHEMATICS   53 ( 3 ) 591 - 619  2016.07  [Refereed]

    　View Summary

    We find presentations by generators and relations for the equivariant quantum co-homology rings of the maximal isotropic Grassmannians of types B, C and D, and we find polynomial representatives for the Schubert classes in these rings. These representatives are given in terms of the same Pfaffian formulas which appear in the theory of factorial P- and Q-Schur functions. After specializing to equivariant co-homology, we interpret the resulting presentations and Pfaffian formulas in terms of Chern classes of tautological bundles.

  • Pieri rule for the factorial $P$-functions

    Takeshi Ikeda, Soojin Cho

    European Mathematical Society Publishing House     25 - 48  2016  [Refereed]

  • Double Schubert polynomials for the classical groups

    Takeshi Ikeda, Leonardo C. Mihalcea, Hiroshi Naruse

    ADVANCES IN MATHEMATICS   226 ( 1 ) 840 - 886  2011.01  [Refereed]

    　View Summary

    For each infinite series of the classical Lie groups of type B, C or D, we construct a family of polynomials parametrized by the elements of the corresponding Weyl group of infinite rank. These polynomials represent the Schubert classes in the equivariant cohomology of the appropriate flag variety. They satisfy a stability property, and are a natural extension of the (single) Schubert polynomials of Billey and Haiman, which represent non-equivariant Schubert classes. They are also positive in a certain sense, and when indexed by maximal Grassmannian elements, or by the longest element in a finite Weyl group, these polynomials can be expressed in terms of the factorial analogues of Schur's Q- or P-functions defined earlier by Ivanov. (C) 2010 Elsevier Inc. All rights reserved.

    DOI J-GLOBAL

Books and Other Publications

  • Lectures on Enumerative Geometry

    IKEDA Takeshi( Part： Sole author)

    University of Tokyo Press  2018.08

Misc

  • Similarity reduction of the modified Yajima-Oikawa equationt

    J. Phys. A 36, no. 45, 11465--11480-   36, no. 45, 11465--11480  2003

    DOI

  • Hierarchy of (2+1)-dimentional nonlinear Shr\"odinger equation, self-dual Yang-Mills equations, and toroidal Lie algebras∫

    Annales Henri Poincar\'e   3(5), 817-845  2002

    DOI

  • Polynomial $\tau$-functions of the NLS-Toda hierarchy and the Virasoro singular vectorsˇ

    Letters in Mathematical Physics›   60, 147-156  2002

    DOI

  • Hierarchy of (2+1)-diveuriral nonlinear Shroudinger equator, self-dual Yang-Mills equations, and toroidal Lie algebras

    Annales Henri Poincare   3(5), 817-845  2002

    DOI

  • Polynomial τ-function of the NLS-Toda hierarchy and the Virasoro singular vectors

    Letters in Mathematical Physics   60, 147-156  2002

    DOI

  • Toroidal Lie algebra and Bogoyaulenshy's 2+1 dimensional equations

    International Mathematics Research Notices   ( 7 )  2001

  • Commuting difference operators arising from the elliptic C-2((1))-face model

    K Hasegawa, T Ikeda, T Kikuchi

    JOURNAL OF MATHEMATICAL PHYSICS   40 ( 9 ) 4549 - 4568  1999.09

    　View Summary

    We study a pair of commuting difference operators arising from the elliptic C-2((1))-face model. The operators, whose coefficients are expressed in terms of the Jacobi's elliptic theta function, act on the space of meromorphic functions on the weight space of the C-2-type simple Lie algebra. We show that the space of functions spanned by the level one characters of the affine Lie algebra <(sp)over cap>(4,C) is invariant under the action of the difference operators.(C) 1999 American Institute of Physics. [S0022-2488(99)03109-6].

    DOI CiNii

  • Coset constructions of conformal blocks

    T Ikeda

    INTERNATIONAL JOURNAL OF MODERN PHYSICS B   11 ( 19 ) 2311 - 2332  1997.07

    　View Summary

    On the basis of the coset construction, we obtained canonical maps that relate the sheaf of conformal blocks of the Wess-Zumino-Witten model to those of the unitarizable Virasoro minimal model. We conjectured that the maps are isomorphisms. Making use of spinor realizations, we confirmed the conjecture for the case of the Ising model. We also discussed the coherency of the sheaf of conformal blocks for the Virasoro algebra.

    DOI

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Research Projects

  • 可積系と関連する代数の表現の研究

  • Integrable systems, Combinatonics, and Rebresentation theory

 

Syllabus

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Social Activities

  • 約分の名人になろう！

    岡山理科大学附属中学校  オープンスクール 

    2018.08
    -