Abstract

Let k be a finite field, a global field, or a local non-archimedean field, and let H₁ and H₂ be split, connected, semisimple algebraic groups over k. We prove that if H₁ and H₂ share the same set of maximal k-tori, up to k-isomorphism, then the Weyl groups W(H₁) and W(H₂) are isomorphic, and hence the algebraic groups modulo their centers are isomorphic except for a switch of a certain number of factors of type B_n and C_n.

(Due to a recent result of Philippe Gille, this result also holds for fields which admit arbitrary cyclic extensions.)

Keywords

maximal tori, algebraic groups

Mathematical Subject Classification

Primary: 20G15

Authors