The essential dimension of the normalizer of a maximal torus in the projective linear group

Abstract

Let $p$ be a prime, $k$ a field of characteristic $\ne p$ and $N$ the normalizer of the maximal torus in the projective linear group ${PGL}_n$. We compute the exact value of the essential dimension ${ed}_k\left(N;p\right)$ of $N$ at $p$ for every $n\ge 1$.