Bulletin of the Belgian Mathematical Society - Simon Stevin

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

Zdeněk Dušek and Oldřich Kowalski

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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

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1347642380

Digital Object Identifier
doi:10.36045/bbms/1347642380

Mathematical Reviews number (MathSciNet)
MR3027358

Zentralblatt MATH identifier
1258.53015

Subjects
Primary: 53A55: Differential invariants (local theory), geometric objects 53B05: Linear and affine connections 16R50: Other kinds of identities (generalized polynomial, rational, involution)

Keywords
Representation of a Lie group invariant function Hilbert basis of~invariants involutive mapping rational mapping

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


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