Cellini's descent algebra and semisimple conjugacy classes of finite groups of Lie type
| dc.creator | Fulman, Jason | |
| dc.date | 1999-09-21 | |
| dc.date | 2000-03-30 | |
| dc.date.accessioned | 2026-07-07T05:30:50Z | |
| dc.date.available | 2026-07-07T05:30:50Z | |
| dc.description | By algebraic group theory, there is a map from the semisimple conjugacy classes of a finite group of Lie type to the conjugacy classes of the Weyl group. Picking a semisimple class uniformly at random yields a probability measure on conjugacy classes of the Weyl group. We conjecture that this measure agrees with a second measure on conjugacy classes of the Weyl group induced by a construction of Cellini which uses the affine Weyl group. This conjecture is confirmed in special cases such as type C odd characteristic and the identity conjugacy class in type A. Models of card shuffling, old and new, arise naturally. Type A shuffles lead to interesting number theory involving Ramanujan sums. It is shown that a proof of our conjecture in type C even characteristic would give an alternate solution to a problem in dynamical systems. An idea is offered for how, at least in type A, to associate to a semisimple conjugacy class an element of the Weyl group, refining the map to conjugacy classes. This is confirmed for the simplest nontrivial example. | |
| dc.description | Very minor revisions; same results | |
| dc.identifier | https://arxiv.org/abs/math/9909121 | |
| dc.identifier | http://arxiv.org/abs/math/9909121 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79127 | |
| dc.subject | Number Theory | |
| dc.subject | Dynamical Systems | |
| dc.title | Cellini's descent algebra and semisimple conjugacy classes of finite groups of Lie type | |
| dc.type | text |