P Amrutha, IISER Thiruvananthapuram


Speaker: P Amrutha, IISER Thiruvananthapuram

Date & Day: September 22, 2022, Thursday Time: 4.00--5.00 pm

Venue: Room 215

Title: On the partitions and multipartitions not divisible by powers of 2


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 for the case of prime numbers. MacDonald’s
paper was a motivation for the McKay conjecture. The announcement of McKay conjecture in 1971
is the origin of a different kind of counting conjectures of finite groups. Extending Macdonald’s

results to all integers is a much harder problem to study. Motivated by a question from chiral rep-
resentations of the wreath products, we will see a generalization of the above question to composite

numbers of the form 2k and a recursive formula for the groups Sn, An, and (Z/rZ)≀ 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.

Room No 215, Department of Mathematics
Thu, September 22, 2022
Start Time
4:00pm-5:00pm IST
1 hour
Created by
Wed, September 21, 2022 1:52pm IST