Updated on 2023/03/22

IKEDA, Takeshi

##### Scopus Paper Info
###### Paper Count: 21  Citation Count: 270  h-index: 9

Click to view the Scopus page. The data was downloaded from Scopus API in March 21, 2023, via http://api.elsevier.com and http://www.scopus.com .

Affiliation
Faculty of Science and Engineering, School of Fundamental Science and Engineering
Job title
Professor
Degree
(BLANK)

Profile

### Research Experience

• 1998.04
-
Now

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

### Education Background

• 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

•

日本数学会

• 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&apos;s Q- or P-functions defined earlier by Ivanov. (C) 2010 Elsevier Inc. All rights reserved.

29
Citation
(Scopus)

### Books and Other Publications

• Lectures on Enumerative Geometry

IKEDA Takeshi( Part： Sole author)

University of Tokyo Press  2018.08

### Research Projects

• 可積系と関連する代数の表現の研究

• Integrable systems, Combinatonics, and Rebresentation theory

### Misc

• Similarity reduction of the modified Yajima-Oikawa equationt

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

• 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

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

Letters in Mathematical Physics›   60, 147-156  2002

• 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

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

Letters in Mathematical Physics   60, 147-156  2002

• 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 &lt;(sp)over cap&gt;(4,C) is invariant under the action of the difference operators.(C) 1999 American Institute of Physics. [S0022-2488(99)03109-6].

• 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.

### Syllabus

• School of Fundamental Science and Engineering

2023   fall quarter

• School of Fundamental Science and Engineering

2023   spring semester

• School of Fundamental Science and Engineering

2023   spring semester

• School of Fundamental Science and Engineering

2023   spring semester

• School of Fundamental Science and Engineering

2023   fall semester

• School of Fundamental Science and Engineering

2023   fall semester

• Graduate School of Fundamental Science and Engineering

2023   fall semester

• Graduate School of Fundamental Science and Engineering

2023   spring semester

• Graduate School of Fundamental Science and Engineering

2023   fall semester

• Graduate School of Fundamental Science and Engineering

2023   spring semester

• Graduate School of Fundamental Science and Engineering

2023   full year

• Graduate School of Fundamental Science and Engineering

2023   spring semester

• Graduate School of Fundamental Science and Engineering

2023   full year

• Graduate School of Fundamental Science and Engineering

2023   full year

• Graduate School of Fundamental Science and Engineering

2023   fall semester

• Graduate School of Fundamental Science and Engineering

2023   spring semester

• Graduate School of Fundamental Science and Engineering

2023   fall semester

• Graduate School of Fundamental Science and Engineering

2023   spring semester

• School of Fundamental Science and Engineering

2023   spring semester

• School of Fundamental Science and Engineering

2023   spring semester

• School of Fundamental Science and Engineering

2023   fall semester

• School of Fundamental Science and Engineering

2023   fall semester

• School of Fundamental Science and Engineering

2023   fall semester

• School of Fundamental Science and Engineering

2023   spring semester

• School of Fundamental Science and Engineering

2023   spring semester

• School of Fundamental Science and Engineering

2023   full year

• School of Fundamental Science and Engineering

2023   full year

• School of Fundamental Science and Engineering

2023   fall semester

• School of Fundamental Science and Engineering

2023   spring semester

• School of Fundamental Science and Engineering

2023   fall semester

• School of Fundamental Science and Engineering

2023   fall semester

• School of Fundamental Science and Engineering

2023   fall semester

• School of Fundamental Science and Engineering

2023   spring semester

• School of Fundamental Science and Engineering

2023   spring semester

• School of Fundamental Science and Engineering

2023   full year

• School of Fundamental Science and Engineering

2023   full year

• School of Fundamental Science and Engineering

2023   full year@fall semester

### 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
-

### Sub-affiliation

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

### Research Institute

• 2022
-
2024

Waseda Research Institute for Science and Engineering   Concurrent Researcher