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

TL;DR

This paper calculates the precise essential dimension at p of the normalizer of a maximal torus in PGLn for all n, providing key insights into the algebraic structure related to projective linear groups.

Contribution

It determines the exact value of the essential dimension at p for the normalizer of a maximal torus in PGLn for all n, a previously unresolved problem.

Findings

Exact values of ed(N;p) for all n

Provides a comprehensive understanding of the algebraic complexity of N

Advances knowledge of essential dimension in algebraic groups

Abstract

Let p be a prime, k be a field of characteristic different from p containing a primitive p-th root of unity and N be the normalizer of the maximal torus in the projective linear group PGLn. We compute the exact value of the essential dimension ed(N;p) of N at p for every n.