Finite reflection groups and linear preserver problems

Chi Kwong Li, Ilya Spitkovsky, Nahum Zobin

Research output: Contribution to journalArticle

Abstract

Let G be one of the Coxeter groups An, Bn, Dn, or I2(n), naturally acting on a Euclidean space V, and let ℒ(G) stand for the set of linear transformations ϕ of End V that satisfy ϕ(G) = G. It is easy to see that ℒ(G) contains all transformations of the form X ↦ PXQ, X ↦ PX*Q, where P, Q belong to the normalizer of G in the orthogonal group and PQ ∈ G. We show that in most cases these transformations exhaust ℒ(G); the only (rather unexpected) exception is the case G = Bn.

Original languageEnglish (US)
Pages (from-to)225-251
Number of pages27
JournalRocky Mountain Journal of Mathematics
Volume34
Issue number1
DOIs
StatePublished - 2004

ASJC Scopus subject areas

  • Mathematics(all)

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