Higman’s conjecture on the number of conjugacy classes of U(n,q)
by
Prof.Igor PAK(UCLA)
→
Europe/Paris
Amphithéâtre Léon Motchane (IHES)
Amphithéâtre Léon Motchane
IHES
Le Bois Marie
35, route de Chartres
91440 Bures-sur-Yvette
Description
In 1960, Higman asked whether the number f(n,q) of conjugacy classes of n x n unitriangular matrices U(n,q) over the finite field with q elements, is polynomial in q for every n. I will survey what is known about this problem, explain the connections to realization spaces of matroids, enumerative combinatorics and group representation theory. I will then describe our recent efforts to prove the conjecture for small n and disprove it for large n.