Statistics/Probability job talk
Date and time: May 25, 2023 (Thursday) 3 to 4 pm
Venue: Ramanujan Hall, Department of Mathematics
Host: Murali K Srinivasan
Speaker: Ashish Mishra
Affiliation: UFPA, Brazil
Title: On quasi Steinberg characters of complex reflection groups
Abstract: 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
χ of G is called a quasi p-Steinberg character if χ(g) is nonzero for every p-regular element
g in G. A quasi p-Steinberg character χ is called weak p-Steinberg if χ has degree |G|p.
These variants of p-Steinberg character were introduced to answer a question of Dipendra
Prasad that asked whether the existence of a weak p-Steinberg character of G implies
that G is a finite group of Lie type. In this joint work with Digjoy Paul and Pooja Singla,
we classify quasi p-Steinberg characters of all finite irreducible complex reflection groups.
In the first part of the talk, we will give an overview of representation theory of complex
reflection groups.