Study on finite-dimensional irreducible modules over a quantum loop algebra via extremal weight modules

2015 Fiscal Year Final Research Report

• Project/Area Number: 25800006
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: Tokyo University of Agriculture and Technology
• Principal Investigator: NAOI Katsuyuki 東京農工大学, 工学(系)研究科(研究院), 講師 (40647898)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 量子アフィン代数 / 古典極限

Outline of Final Research Achievements

In this research, we have studied the structure of finite-dimensional modules over an infinite-dimensional algebra called quantum loop algebra, by focusing their classical limits. Here classical limits of a module over a quantum loop algebra is a module over an affine Lie algebra which is obtained by taking a certain specialization.
As results of this research, we have described the detailed structures of special simple modules called minimal affinizations. In addition, we have also studied the noncommutativity between the operations of taking tensor products and of taking classical limits.

Free Research Field

数学