The braid group surjects onto $G_2$ tensor space
| Autor: | Morrison, Scott |
|---|---|
| Rok vydání: | 2009 |
| Předmět: | |
| Zdroj: | Pacific Journal of Mathematics 249-1 (2011), 189--198 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.2140/pjm.2011.249.189 |
| Popis: | Let V be the 7-dimensional irreducible representation of the quantum group U_q(g_2). For each n, there is a map from the braid group B_n to the endomorphism algebra of the n-th tensor power of V, given by R-matrices. We can extend this linearly to a map on the braid group algebra. Lehrer and Zhang (MR2271576) prove this map is surjective, as a special case of a more general result. Using Kuperberg's spider for G_2 from arXiv:math.QA/9201302, we give an elementary diagrammatic proof of this result. Comment: 9 pages |
| Databáze: | arXiv |
| Externí odkaz: |
|