Separating invariants and finite reflection groups

TY - JOUR

T1 - Separating invariants and finite reflection groups

AU - Dufresne, Emilie

PY - 2009/8/20

Y1 - 2009/8/20

N2 - A separating algebra is, roughly speaking, a subalgebra of the ring of invariants whose elements distinguish between any two orbits that can be distinguished using invariants. In this paper, we introduce a geometric notion of separating algebra. This allows us to prove that only groups generated by reflections may have polynomial separating algebras, and only groups generated by bireflections may have complete intersection separating algebras.

AB - A separating algebra is, roughly speaking, a subalgebra of the ring of invariants whose elements distinguish between any two orbits that can be distinguished using invariants. In this paper, we introduce a geometric notion of separating algebra. This allows us to prove that only groups generated by reflections may have polynomial separating algebras, and only groups generated by bireflections may have complete intersection separating algebras.

KW - Bireflections

KW - Complete intersection ring

KW - Finite groups

KW - Invariant theory

KW - Polynomial ring

KW - Reflections

KW - Separating invariants

UR - http://www.scopus.com/inward/record.url?scp=67349147894&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2009.03.013

DO - 10.1016/j.aim.2009.03.013

M3 - Article

AN - SCOPUS:67349147894

SN - 0001-8708

VL - 221

SP - 1979

EP - 1989

JO - Advances in Mathematics

JF - Advances in Mathematics

IS - 6

ER -