Rational involutive automorphisms related with standard representations of SL(2,R)

Abstract

Standard irreducible representations of the group SL(2,R) on coefficients of homogeneous polynomials in two variables are studied in a new context. It is proved that any standard representation of SL(2,R) on R^(n+1) induces an involutive rational mapping of an open dense subset of R^(n+1) onto itself.

Examples in low dimensions are presented. We also construct formal involutive rational mappings with "arbitrary complexity".

Keywords

• Rational
• involutive
• automorphisms
• related
• with
• standard
• representations
• SL2,R