Algebraic analysis of integrable models

2014 Fiscal Year Final Research Report

• Project/Area Number: 23340039
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Global analysis
• Research Institution: Rikkyo University
• Principal Investigator: JIMBO Michio 立教大学, 理学部, 教授 (80109082)
• Project Period (FY): 2011-04-01 – 2015-03-31
• Keywords: フェルミオン基底 / ６頂点模型 / サイン・ゴルドンモデル / 形状因子 / ボレル部分代数 / 量子トロイダル代数 / ベーテ仮説

Outline of Final Research Achievements

The main achievements are the following.(1) We identified the continuum limit of our fermionic basis in solvable lattice models with those employed previously in the enumeration of form factors, thereby establishing the fermionic picture in field theory. (2) We studied representations in “category O” of Borel subalgebras of quantum affine algebras, and classified the irreducible objets by highest weights. (3) We constructed a family of irreducible representations of quantum toroidal algebras by an elementary method. We also diagonalized the transfer matrix acting on the Fock space, and established the Bethe ansatz.

Free Research Field

数理物理学