Combinatorics arising from modular representations of symmetric groups

• Project/Area Number: 24540020
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Okayama University
• Principal Investigator: YAMADA HiroFumi 岡山大学, 自然科学研究科, 教授 (40192794)
• Co-Investigator(Renkei-kenkyūsha): MIZUKAWA Hiroshi 防衛大学校, 数学教育室, 准教授 (60531762)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000); Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000); Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000); Fiscal Year 2012: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
• Keywords: シューア函数 / ヤング図形 / 対称群 / 分割数 / 指標表 / アフィンリー環 / 岩堀ヘッケ間 / Q函数 / 岩堀ヘッケ代数 / アフィンリー代数 / カルタン行列

Outline of Final Research Achievements

We derived the determinant of the matrices related to the character tables of the symmetric groups. We also gave a (q,t) analogue of a well-known partition identity. In connection with the affine Lie algebras, we found an interesting Schur function identities, which arose from the basic representation of the affine Lie algebra.

Research Products

• [Journal Article] Arithmetic identities for class regular partitions (2016)
  • Author(s): H. Mizukawa and HF. Yamada
  • Journal Title: Hokkaido Math. J Volume: 45
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Schur function identities arising from the basic representation of A(2,2) (2015)
  • Author(s): H. Mizukawa, T. Nakajima, R. Seno and HF. Yamada
  • Journal Title: Lett. Math. Phys Volume: 104 Pages: 1317-1331
  • Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Schur function identities arising from the basic representation of A(2)(2) (2014)
  • Author(s): H.Mizukawa, T.Nakajima, R.Seno and H.-F.Yamada
  • Journal Title: Letters in Mathematical Physics Volume: 104 Pages: 1317-1331
  • Peer Reviewed
• [Journal Article] Combinatorics for graded Cartan matrices of the Iwahori-Hecke algebra of type A (2013)
  • Author(s): M. Ando, T. Suzuki and HF. Yamada
  • Journal Title: Annals of Combinatorics Volume: 17 Pages: 427-442
  • Peer Reviewed
• [Journal Article] Combinatorics of graded Cartan matrices of the Iwahori-Hecke algebra oftype A (2013)
  • Author(s): Masanori ANDO, Takeshi SUZUKI and Hiro-Fumi YAMADA
  • Journal Title: Annals of Combinatorics Volume: 17 Pages: 1-16
  • Peer Reviewed
• [Presentation] Combinatorics of regular partitions and character tables of the symmetric groups (2014)
  • Author(s): H.-F. Yamada
  • Organizer: International Conference on Algebraic Combinatorics
  • Place of Presentation: RIMS, Kyoto Unoversity
  • Year and Date: 2014-12-18
  • Invited
• [Presentation] Rectangular Schur functions and trapezoidal Q-functions
  • Author(s): HF. Yamada
  • Organizer: Shanghai Workshop on Representation Theory
  • Place of Presentation: Shanghai, China
  • Invited
• [Presentation] 分割の組合せ論
  • Author(s): 山田裕史
  • Organizer: 研究集会「代数解析学の未来」
  • Place of Presentation: 早稲田大学
  • Invited
• [Presentation] 分割の組合せ論
  • Author(s): 山田裕史
  • Organizer: 研究集会「代数群と量子群」
  • Place of Presentation: 北見工業大学
  • Invited
• [Presentation] A combinatorics of partitions
  • Author(s): 山田裕史
  • Organizer: Workshop on Algebra, Analysis and Geometry
  • Place of Presentation: 鹿児島大学
  • Invited