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''.
Citation
Zdeněk Dušek. Oldřich Kowalski. "Rational involutive automorphisms related with standard representations of ${\mathrm{SL}}(2,\mathbb R)$." Bull. Belg. Math. Soc. Simon Stevin 19 (3) 523 - 533, september 2012. https://doi.org/10.36045/bbms/1347642380
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