Date and time : August 29, Monday, 3.30-4.30 pm
Venue : Seminar Hall
ON THE DEGREES OF REPRESENTATIONS OF GROUPS NOT DIVISIBLE BY 2^k
Given a finite group G and a natural number p, an interesting question one can ask is to count the number of inequivalent irreducible representations of G whose degree is not divisible by p.This question originated in a paper by I. G. Macdonald on the case of prime numbers. Extending Macdonald’s results to all integers is a much harder problem to study. Motivated by a question from chiral representations of the wreath products, we will see a generalization of the above question to composite numbers of the form 2^k and a recursive formula for the groups Sn, An, and Zr≀Sn. Regardless of the description of the count, even for the smaller integers, a complete characterization of the irreducibles with a degree not divisible by a given prime number is still missing in the literature. We will see such characterization for some special cases at the end and further open problems in this direction. This is joint work with T. Geetha.