TY - JOUR

T1 - Finite reflection groups and linear preserver problems

AU - Li, Chi Kwong

AU - Spitkovsky, Ilya

AU - Zobin, Nahum

PY - 2004

Y1 - 2004

N2 - 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.

AB - 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.

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U2 - 10.1216/rmjm/1181069902

DO - 10.1216/rmjm/1181069902

M3 - Article

AN - SCOPUS:2942662107

SN - 0035-7596

VL - 34

SP - 225

EP - 251

JO - Rocky Mountain Journal of Mathematics

JF - Rocky Mountain Journal of Mathematics

IS - 1

ER -