Séminaire de Mathématique

Higman’s conjecture on the number of conjugacy classes of U(n,q)

by Prof. Igor PAK (UCLA)

Amphithéâtre Léon Motchane (IHES)

Amphithéâtre Léon Motchane


Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette
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.

Joint work with Andrew Soffer.