KEIO RESEARCHERS INFORMATION SYSTEM

Career 【 Display / hide 】

Career 【 Display / hide 】

• 2010.04

  -

  2011.03

  The University of Tokyo, Graduate School of Mathematical Sciences, 学振PD

• 2011.04

  -

  2012.03

  Rikkyo University, College of Science, 学振PD

• 2012.04

  -

  2013.03

  Aoyama Gakuin University, College of Science and Engineering, 助手

• 2013.04

  -

  2017.03

  Aoyama Gakuin University, College of Science and Engineering, 助教

• 2017.04

  -

  2022.03

  Tokai University, School of Science, 講師

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Research Areas 【 Display / hide 】

Research Areas 【 Display / hide 】

• Natural Science / Algebra (Algebraic combinatorics)

• Natural Science / Basic mathematics

• Natural Science / Mathematical physics and fundamental theory of condensed matter physics ((classical/quantum) integrable systems)

Research Keywords 【 Display / hide 】

Research Keywords 【 Display / hide 】

• Combinatorics on Young diagrams

• Tropical Geometry

• Bethe equations

• Classical integrable systems

• Symmetric polynomials

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Books 【 Display / hide 】

Books 【 Display / hide 】

• ヤング盤の組合せ論 : 非可換シューア関数入門 = Combinatorics of young tableaux : an introduction to noncommutative schur functions

  岩尾, 慎介, 共立出版, 2025.07,  Page： iv, 181p

  • CiNii Research

• Young tableaux

  William Fulton (origi, Takeshi Ikeda, Rei Inoue, Shinsuke Iwao, 丸善出版, 2019.06

  Scope: Translation

Papers 【 Display / hide 】

Papers 【 Display / hide 】

• Free fermionic probability theory and k-theoretic schubert calculus

  Shinsuke Iwao, Kohei Motegi, Travis Scrimshaw

  Forum of Mathematics, Sigma  2025

  Accepted

  • Access to Document (DOI)

• Tetrahedron equation and Schur functions

  Shinsuke Iwao, Kohei Motegi, Ryo Ohkawa

  Journal of Physics A: Mathematical and Theoretical  2024.11

  Accepted

  • Access to Document (DOI)

• Closed k-Schur Katalan functions as K-homology Schubert representatives of the affine Grassmannian

  Takeshi Ikeda, Shinsuke Iwao, Satoshi Naito

  Transactions of the American Mathematical Society, Series B  2024.03

  Accepted,  ISSN  2330-0000

  　View Summary

  <p>Recently, Blasiak–Morse–Seelinger introduced symmetric func- tions called Katalan functions, and proved that the <inline-formula content-type="math/mathml">
  <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper K">
  <mml:semantics>
  <mml:mi>K</mml:mi>
  <mml:annotation encoding="application/x-tex">K</mml:annotation>
  </mml:semantics>
  </mml:math>
  </inline-formula>-theoretic <inline-formula content-type="math/mathml">
  <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="k">
  <mml:semantics>
  <mml:mi>k</mml:mi>
  <mml:annotation encoding="application/x-tex">k</mml:annotation>
  </mml:semantics>
  </mml:math>
  </inline-formula>-Schur functions due to Lam–Schilling–Shimozono form a subfamily of the Katalan functions. They conjectured that another subfamily of Katalan functions called closed <inline-formula content-type="math/mathml">
  <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="k">
  <mml:semantics>
  <mml:mi>k</mml:mi>
  <mml:annotation encoding="application/x-tex">k</mml:annotation>
  </mml:semantics>
  </mml:math>
  </inline-formula>-Schur Katalan functions is identified with the Schubert structure sheaves in the <inline-formula content-type="math/mathml">
  <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper K">
  <mml:semantics>
  <mml:mi>K</mml:mi>
  <mml:annotation encoding="application/x-tex">K</mml:annotation>
  </mml:semantics>
  </mml:math>
  </inline-formula>-homology of the affine Grassmannian. Our main result is a proof of this conjecture.</p>
  
  <p>We also study a <inline-formula content-type="math/mathml">
  <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper K">
  <mml:semantics>
  <mml:mi>K</mml:mi>
  <mml:annotation encoding="application/x-tex">K</mml:annotation>
  </mml:semantics>
  </mml:math>
  </inline-formula>-theoretic Peterson isomorphism that Ikeda, Iwao, and Maeno constructed, in a nongeometric manner, based on the unipotent solution of the relativistic Toda lattice of Ruijsenaars. We prove that the map sends a Schubert class of the quantum <inline-formula content-type="math/mathml">
  <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper K">
  <mml:semantics>
  <mml:mi>K</mml:mi>
  <mml:annotation encoding="application/x-tex">K</mml:annotation>
  </mml:semantics>
  </mml:math>
  </inline-formula>-theory ring of the flag variety to a closed <inline-formula content-type="math/mathml">
  <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper K">
  <mml:semantics>
  <mml:mi>K</mml:mi>
  <mml:annotation encoding="application/x-tex">K</mml:annotation>
  </mml:semantics>
  </mml:math>
  </inline-formula>-<inline-formula content-type="math/mathml">
  <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="k">
  <mml:semantics>
  <mml:mi>k</mml:mi>
  <mml:annotation encoding="application/x-tex">k</mml:annotation>
  </mml:semantics>
  </mml:math>
  </inline-formula>-Schur Katalan function up to an explicit factor related to a translation element with respect to an antidominant coroot. In fact, we prove this map coincides with a map whose existence was conjectured by Lam, Li, Mihalcea, Shimozono, and proved by Kato, and more recently by Chow and Leung.</p>

  • Access to Document (DOI)

• Free fermions and canonical Grothendieck polynomials

  Shinsuke Iwao, Kohei Motegi, Travis Scrimshaw

  Algebraic Combinatorics 7 ( 1 ) 245 - 274 2024.02

  Accepted,  ISSN  2589-5486

  　View Summary

  We give a presentation of refined (dual) canonical Grothendieck polynomials and their skew versions using free fermions. Using this, we derive a number of identities, including the skew Cauchy identities, branching rules, expansion formulas, and integral formulas.

  • Access to Document (DOI)

• Free fermions and Schur expansions of multi-Schur functions

  Shinsuke Iwao

  Journal of Combinatorial Theory. Series A 198 2023.08

  Accepted,  ISSN  0097-3165

  　View Summary

  Multi-Schur functions are symmetric functions that generalize the supersymmetric Schur functions, the flagged Schur functions, and the refined dual Grothendieck functions, which have been intensively studied by Lascoux. In this paper, we give a new free-fermionic presentation of them. The multi-Schur functions are indexed by a partition and two “tuples of tuples” of indeterminates. We construct a family of linear bases of the fermionic Fock space that are indexed by such data and prove that they correspond to the multi-Schur functions through the boson-fermion correspondence. By focusing on some special bases, which we call refined bases, we give a straightforward method of expanding a multi-Schur function in the refined dual Grothendieck polynomials. We also present a sufficient condition for a multi-Schur function to have its Hall-dual function in the completed ring of symmetric functions.

  • Access to Document (DOI)

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Reviews, Commentaries, etc. 【 Display / hide 】

Reviews, Commentaries, etc. 【 Display / hide 】

• On flagged K-theoretic symmetric polynomials

  Shinsuke Iwao

  RIMS Kokyuroku 2258   48 - 56 2023.06

  Lead author

• Free-fermions and canonical Grothendieck polynomials

  Shinsuke Iwao, Kohei Motegi, Travis Scrimshaw

   2022.11

  　View Summary

  We give a presentation of refined (dual) canonical Grothendieck polynomials
  and their skew versions using free-fermions. Using this, we derive a number of
  identities, including the skew Cauchy identities, branching rules, expansion
  formulas, and integral formulas.
  

• Noncommutative Schur Function

  岩尾慎介

  数理科学 (サイエンス社)  57 ( 8 ) 34 - 42 2019.08

  Lead author,  ISSN  0386-2240

  • CiNii Research

• ボゾンフェルミオン対応の基礎と線形代数のみから双対GROTHENDIECK多項式の行列式表示を導く

  Iwao, Shinsuke

  RIMS Kokyuroku (京都大学数理解析研究所)  2071   125 - 133 2018.04

  ISSN  1880-2818

  　View Summary

  Grothendieck多項式とは, 旗多様体の量子K理論を表現する際に現れる対称多項式であり, Schubert多項式のK理論版ということができる. Schubert多項式同様, Grothendieck多項式は対称群の元によりパラメータ付けされている. 特にGrassmannian置換に対応するGrothendieck多項式は, Schur多項式のK理論版といえる. ここでは, Grassmann置換に対応するGrothendieck多項式のみを扱う. 本稿では, ボゾンフェルミオン対応を用いて, Grothendieck多項式と双対Grothendieck多項式の特徴づけを与える. 応用として, 双対Grothendieck多項式の行列式表示を与える.

  • CiNii Research

• Peterson Isomorphism in $K$-theory and Relativistic Toda Lattice

  Takeshi Ikeda, Shinsuke Iwao, Toshiaki Maeno

   2017.03

  　View Summary

  The $K$-homology ring of the affine Grassmannian of $SL_n(C)$ was studied by Lam, Schilling, and Shimozono. It is realized as a certain concrete Hopf subring of the ring of symmetric functions. On the other hand, for the quantum $K$-theory of the flag variety $Fl_n$, Kirillov and Maeno provided a conjectural presentation based on the results obtained by Givental and Lee. We construct an explicit birational morphism between the spectrums of these two rings. Our method relies on Ruijsenaars's relativistic Toda lattice with unipotent initial condition. From this result, we obtain a $K$-theory analogue of the so-called Peterson isomorphism for (co)homology. We provide a conjecture on the detailed relationship between the Schubert bases, and, in particular, we determine the image of Lenart--Maeno's quantum Grothendieck polynomial associated with a Grassmannian permutation.

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Presentations 【 Display / hide 】

Presentations 【 Display / hide 】

• Exact solutions to the TASEP Bethe equation.

  岩尾慎介

  非線形波動から可積分系へ2025, 

  2025.10

  -

  2025.11

  , 

  Oral presentation (general)

• An algebro-geometric approach to the Bethe roots of the periodic TASEP

  Shinsuke Iwao

  [International presentation]  ISQS 29 (Prague) , 

  2025.07

  , 

  Oral presentation (general)

• The relativistic Toda Lattice and quantum K-Schubert classes of the flag variety

  Shinsuke Iwao

  Discrete integrable systems: difference equations, cluster algebras and probabilistic models, 

  2024.10

  -

  2024.11

  , 

  Oral presentation (general)

• The relativistic Toda Lattice and quantum K-Schubert Classes of a Flag Manifold

  Shinsuke Iwao

  可積分系数理の新展開, 

  2024.09

  , 

  Oral presentation (general)

• The relativistic Toda Lattice and quantum K-Schubert Classes of Flag Manifolds

  Shinsuke Iwao

  Workshop on Integrable Systems and Cluster Algebras, 

  2024.09

  , 

  Oral presentation (general)

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Research Projects of Competitive Funds, etc. 【 Display / hide 】

Research Projects of Competitive Funds, etc. 【 Display / hide 】

• Geometric aspects of the free-fermion and the non-commutative Schur functions

  2023.04

  -

  2027.03

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), No Setting

• 量子 K 理論のシューベルト・カルキュラスとピーターソン同型

  2022.04

  -

  2027.03

  日本学術振興会, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), No Setting

  　View Summary

  A 型ルート系については， K 理論的ピーターソン同型が，ごく最近になって，明示的な形で確立された．アフィン側のシューベルト類を表す closed K-k-Schur functions の明示公式も示すことができた．この結果を利用して，シュバレー規則の帰結や，アフィン側のピエリ規則による量子側への帰結などを詳しく検討することができる．
  <BR>
  C 型の場合， Seelinger によって， アフィングラスマン多様体の homology シューベルト類に対する明示公式が予想されている．この予想を，K 理論に拡張した形で解決し，そこから導き出されることを探求する．

• Tropical mathematics and combinatorics on Young tableaux

  2019.04

  -

  2023.03

  MEXT,JSPS, Grant-in-Aid for Scientific Research, IWAO Shinsuke, Grant-in-Aid for Scientific Research (C), Principal investigator

  　View Summary

  This study develops a new framework that bridges classical integrable systems, a class of differential equations, with the modern geometric technique of “quantum K-theory.” Quantum K-theory extends the cohomology theory of geometry into an algebraic toolkit for computing the structure of shapes (topology). Focusing on the flag variety, a geometric object of key importance in mathematical physics, we investigate its quantum K-theory. As a result, we identify that the classical integrable system corresponding to the quantum K-theory of the flag variety is the relativistic Toda equation.

• Study of integrable systems and tropical curves

  2014.04

  -

  2018.03

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Iwao Shinsuke, Grant-in-Aid for Young Scientists (B), No Setting

  　View Summary

  The tropical geometry is a kind of geometry where the usual multiplication and addition are replaced with the addition and maximum. Since it has been known that the tropical geometry admits good applications to the study of integrable system theory, the main aim of this research is to study their essential relations. The main results of this research are as follows: 1. The relation between the "quantum K-theory" of the flag variety and some special symmetric polynomials are clarified by using the algebraic method to the relativistic Toda equation. 2. The application of the tropical KP equation to various combinatoric problems of Young tableau is obtained.

• Integrable system study of the theory and tropical curve

  2014.04

  -

  2018.03

  Japan Society for the Promotion of Science, 若手研究（B), Shinsuke Iwao, Principal investigator

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Courses Taught 【 Display / hide 】

Courses Taught 【 Display / hide 】

• MATHEMATICAL COMBINATORICS

  2025

• LINEAR ALGEBRA

  2025

• GENERAL EDUCATION SEMINAR (DB)

  2025

• GENERAL EDUCATION SEMINAR (DA)

  2025

• DIFFERENTIAL AND INTEGRAL CALCULUS

  2025

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Committee Experiences 【 Display / hide 】

Committee Experiences 【 Display / hide 】

• 2020.04

  -

  2021.03

  Local representative, Mathematical society of Japan