In these notes we investigate the rings of real polynomials in four
variables, which are invariant under the action of the reflectiongroups [3,4,3]
and [3,3,5]. It is well known that they are rationally generated in degree
2,6,8,12 and 2,12,20,30. We give a different proof of this fact by giving
explicit equations for the generating polynomials.Comment: 10 page

Sarti, Alessandra

English

arXiv

2000 Mathematics Subject Classification: Primary 20F55, 13F20; Secondary 14L30.We construct invariant polynomials for the reflection groups
[3, 4, 3] and [3, 3, 5] by using some special sets of lines on the quadric P1 × P1
in P3. Then we give a simple proof of the well known fact that the ring of
invariants are rationally generated in degree 2,6,8,12 and 2,12,20,30

A geometrical construction for the polynomial invariants of some reflection groups

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