IMSc Webinar

Generating function for the powers in $\text{GL}(n,q)$

Rijubrata Kundu

IISER Pune

Zoom link: us02web.zoom.us/j/86865846431

Let $M\geq 2$ be any integer. Consider the set
$\text{GL}(n,q)^M=\{x^M|x\in \text{GL}(n,q)\}$, which
is the set of all $M^{th}$ powers in the group $\text{GL}(n,q)$. In this talk, we will obtain generating functions for


(a) the proportion of regular and regular semsimple elements in
$\text{GL}(n,q)^M$, assuming $(M,q)=1$,


(b) the proportion of semisimple and all elements which are $M^{th}$ powers when $(M,q)=1$, and $M$ is a power of a prime.

Time permitting we will also discuss the other extreme, where we assume $M$ is a prime and $q$ is a power of $M$.

This is a joint work with Dr. Anupam Singh.