Ｓｃｈｕｂｅｒｔ加群の構造の研究

• Project/Area Number: 15J05373
• Research Category: Grant-in-Aid for JSPS Fellows
• Allocation Type: Single-year Grants
• Section: 国内
• Research Field: Algebra
• Research Institution: The University of Tokyo
• Principal Investigator: 渡部 正樹 東京大学, 数理科学研究科, 特別研究員(PD)
• Project Period (FY): 2015-04-24 – 2017-03-31
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥2,170,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥270,000); Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2015: ¥1,000,000 (Direct Cost: ¥1,000,000)
• Keywords: Schubert多項式 / Kraskiewicz-Pragacz加群 / 最高ウェイト圏 / 最高ウエイト圏

Outline of Annual Research Achievements

Schubert多項式の性質について、Kraskiewicz-Pragacz加群を用いた表現論的なアプローチによる研究を行った。本年度は、skew divided difference operatorとSchubert多項式についてのKirillovによる正値性の予想を主な目標として、Kraskiewicz-Pragacz加群やSamによるこれのdouble Schubert多項式での類似物などを使って研究を行ったが、よい成果が得られなかった。
昨年度までの研究で得られた成果について、国内外の学会やセミナーに幅広く参加し、研究発表を行った。

Research Progress Status

28年度が最終年度であるため、記入しない。

Strategy for Future Research Activity

28年度が最終年度であるため、記入しない。

Research Products

• [Journal Article] Kraskiewicz-Pragacz modules and Pieri and dual Pieri rules for Schubert polynomials (2017)
  • Author(s): Masaki Watanabe
  • Journal Title: Journal of Mathematical Sciences, the University of Tokyo Volume: 24 Pages: 259-270
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] An approach toward Schubert positivities of polynomials using Kraskiewicz-Pragacz modules (2016)
  • Author(s): Masaki Watanabe
  • Journal Title: European Journal of Combinatorics Volume: 58C Pages: 17-33
  • DOI: 10.1016/j.ejc.2016.04.010
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Kraskiewicz-Pragacz modules and Ringel duality (2016)
  • Author(s): Masaki Watanabe
  • Journal Title: Journal of Algebra Volume: 468 Pages: 1-23
  • DOI: 10.1016/j.jalgebra.2016.07.025
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Tensor product of Kraskiewicz-Pragacz modules (2015)
  • Author(s): Masaki Watanabe
  • Journal Title: Journal of Algebra Volume: 443 Pages: 422-429
  • DOI: 10.1016/j.jalgebra.2015.07.006
  • Peer Reviewed
• [Presentation] Schubert polynomials and Kraskiewicz-Pragacz modules (2016)
  • Author(s): Masaki Watanabe
  • Organizer: Geometric Representation Theory
  • Place of Presentation: 京都大学（京都府・京都市）
  • Year and Date: 2016-10-10
• [Presentation] Schubert polynomials, Kraskiewicz-Pragacz modules and quasi-hereditary algebras (2016)
  • Author(s): Masaki Watanabe
  • Organizer: Summer School on Quasi-hereditary Algebras
  • Place of Presentation: 大阪府立大学（大阪府・堺市）
  • Year and Date: 2016-08-28
• [Presentation] Kraskiewicz-Pragacz modules and Pieri and dual Pieri rules for Schubert polynomials (2016)
  • Author(s): Masaki Watanabe
  • Organizer: FPSAC 2016
  • Place of Presentation: Simon Fraser University, Vancouver (Canada)
  • Year and Date: 2016-07-05
  • Int'l Joint Research
• [Presentation] Kraskiewicz-Pragacz modules and some positivity properties of Schubert polynomials (2015)
  • Author(s): Masaki Watanabe
  • Organizer: Shanghai Conference on Representation Theory
  • Place of Presentation: Tian He Hotel, Chongming Island, Shanghai, China
  • Year and Date: 2015-12-09
  • Int'l Joint Research
• [Presentation] Kraskiewicz-Pragacz modules and some positivity properties of Schubert polynomials (2015)
  • Author(s): Masaki Watanabe
  • Organizer: 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
  • Place of Presentation: KAIST, Daejeon, Korea
  • Year and Date: 2015-07-07
  • Int'l Joint Research