Carlos André "Gutkin's conjecture for locally profinite algebra groups"

Let A be a finite-dimensional nilpotent algebra over a self-dual field K, let G = 1+A be the algebra group associated with A, and let V be a unitary irreducible G-module. In 1973, E.A. Gutkin claimed to have proved that there exists a subalgebra B of A such that V is induced from a one-dimensional unitary representation W of the algebra subgroup H = 1+B. A correct proof of this statement has been given in 2004 by Z. Halasi in the case where K is a finite field, and in 2011 by M. Boyarchenko in the general case. In this talk, we discuss Gutkin's conjecture in more general situations, and show how Boyarchenko's methods can be extend to the case where G is the unit group of a split basic algebra over K, or a group of fixed points of an involution defined on A.

This is joint work with João Dias.

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