Verification of the GGS conjecture for sl(n), n <= 12
| dc.creator | Schedler, Travis | |
| dc.date | 1999-01-19 | |
| dc.date | 1999-08-02 | |
| dc.date.accessioned | 2026-07-07T05:27:35Z | |
| dc.date.available | 2026-07-07T05:27:35Z | |
| dc.description | In the 1980's, Belavin and Drinfeld classified non-unitary solutions of the classical Yang-Baxter equation (CYBE) for simple Lie algebras. They proved that all such solutions fall into finitely many continuous families and introduced combinatorial objects to label these families, Belavin-Drinfeld triples. In 1993, Gerstenhaber, Giaquinto, and Schack attempted to quantize such solutions for Lie algebras sl(n). As a result, they formulated a conjecture stating that certain explicitly given elements R satisfy the quantum Yang-Baxter equation (QYBE) and the Hecke condition. Specifically, the conjecture assigns a family of such elements R to any Belavin-Drinfeld triple of type A_{n-1}. Until recently, this conjecture has only been known to hold for n <= 4. In 1998 Giaquinto and Hodges checked the conjecture for n=5 by direct computation using Mathematica. Here we report a computation which allowed us to check that the conjecture holds for n <= 10. The program is included which prints an element R for any triple and checks that R satisfies the QYBE and Hecke conditions. | |
| dc.description | revised: proven for n <= 12. also includes version 2 of the GGS test program, which is faster and more efficient. the program code is after \end{document} in the source (download as plain text). For the author's latest results on the GGS conjecture, see math.QA/9903079 | |
| dc.identifier | https://arxiv.org/abs/math/9901079 | |
| dc.identifier | http://arxiv.org/abs/math/9901079 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77973 | |
| dc.subject | Quantum Algebra | |
| dc.title | Verification of the GGS conjecture for sl(n), n <= 12 | |
| dc.type | text |