✦ LIBER ✦
BGP-Reflection Functors and Lusztig's Symmetries: A Ringel–Hall Algebra Approach to Quantum Groups
✍ Scribed by Jie Xiao; Shilin Yang
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 303 KB
- Volume
- 241
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
✦ Synopsis
According to the canonical isomorphisms between the Ringel᎐Hall algebras Ž . composition algebras and the quantum groups, we deduce Lusztig's symmetries T Y , i g I, by applying the Bernstein ᎐Gelfand᎐Ponomarev reflection functors to i, 1 the Drinfeld doubles of Ringel᎐Hall algebras. The fundamental properties of T Y i, 1 Ž . Y including the following can be obtained conceptually. 1 T , i g I induce autoi, 1 Ž .
Ž . Y morphisms of the quantum groups U ᒄ and on the integrable modules. 2 T , q i , 1 i g I satisfy the braid group relations. This extends and completes the results of B. Ž .