Generic groups over generic finite fields
主 题: Generic groups over generic finite fields
报告人: Professor Michel Broué (Université Paris Diderot Paris 7)
时 间: 2013-06-07 14:00-15:00
地 点: 理科一号楼1114（数学所活动）
Let GLn(q) be the group of invertible n x n matrices with entries in the finite field with q elements. The order of GLn(q) is the value at x = q of the polynomial.
Not only orders of "natural subgroups", but also Sylow theorems, dimensions of irreducible (complex) representations, and even modular representation theory (representations in nonzero characteristic) of GLn(q) may as well be described by polynomials evaluated at q. As if there were an object "GLn(x)" which would specialize to GLn(q) for x = q.
Same phenomena occur for other finite groups of Lie type over finite fields, attached to the other Weyl groups.
It is then natural to try to construct similar polynomial data attached to other finite
Coxeter groups, and even to finite groups generated by pseudo-reections : this is the
program named "Spetses". We hope to say a few words about the current state of that