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

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''.

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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

Information

Published: september 2012
First available in Project Euclid: 14 September 2012

zbMATH: 1258.53015
MathSciNet: MR3027358
Digital Object Identifier: 10.36045/bbms/1347642380

Subjects:
Primary: 16R50, 53A55, 53B05

Rights: Copyright © 2012 The Belgian Mathematical Society

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Vol.19 • No. 3 • september 2012
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