## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Rational involutive automorphisms related with standard representations of ${\mathrm{SL}}(2,\mathbb R)$

#### Abstract

Standard irreducible representations of the group $\mathrm{SL}(2,\mathbb R)$ on coefficients of homogeneous polynomials in two variables are studied in a new context. It is proved that any standard representation of $\mathrm{SL}(2,\mathbb R)$ on $\mathbb R^{n+1}$ induces an involutive rational mapping of an open dense subset of $\mathbb R^{n+1}$ onto itself. Examples in low dimensions are presented. We also construct formal involutive rational mappings with arbitrary complexity''.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 19, Number 3 (2012), 523-533.

Dates
First available in Project Euclid: 14 September 2012

https://projecteuclid.org/euclid.bbms/1347642380

Digital Object Identifier
doi:10.36045/bbms/1347642380

Mathematical Reviews number (MathSciNet)
MR3027358

Zentralblatt MATH identifier
1258.53015

#### Citation

Dušek, Zdeněk; Kowalski, Oldřich. Rational involutive automorphisms related with standard representations of ${\mathrm{SL}}(2,\mathbb R)$. Bull. Belg. Math. Soc. Simon Stevin 19 (2012), no. 3, 523--533. doi:10.36045/bbms/1347642380. https://projecteuclid.org/euclid.bbms/1347642380