Hall 123

On quasi Steinberg characters of complex reflection groups

Ashish Mishra

UFPA, Brazil

Consider a finite group G and a prime number p dividing the order
of G. A p-regular element of G is an element whose order is coprime to p. An
irreducible character $\chi$ of G is called a quasi p-Steinberg character
if $\chi(g)$ is nonzero for every p-regular element $g$ in G. The quasi
p-Steinberg character is a generalization of the well-known p-Steinberg
character. A group, which does not have a non-linear quasi p-Steinberg
character, can not be a finite group of Lie type of characteristic p.
Therefore, it is natural to ask for the classification of all non-linear
quasi p-Steinberg characters of any finite group G. In this joint work with
Digjoy Paul and Pooja Singla, we classify quasi p-Steinberg characters of
all finite complex reflection groups.