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A SL(2) covariant theory of genus 2 hyperelliptic functions

Published online by Cambridge University Press:  18 February 2004

CHRIS ATHORNE ,
J. C. EILBECK  and
V. Z. ENOLSKII
CHRIS ATHORNE
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW. e-mail: c.athorne@maths.gla.ac.uk
J. C. EILBECK
Affiliation:
Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS. e-mail: J.C.Eilbeck@hw.ac.uk
V. Z. ENOLSKII
Affiliation:
Dipartimento di Fisica “E. R. Caianiello”, Universita di Salerno, Via S. Allende, 84081 Baronissi (SA), Italy. e-mail: vze@ma.hw.ac.uk
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Abstract

We present an algebraic formulation of genus 2 hyperelliptic functions which exploits the underlying covariance of the family of genus 2 curves. This allows a simple interpretation of all identities in representation theoretic terms. We show how the classical theory is recovered when one branch point is moved to infinity.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 136 , Issue 2 , March 2004 , pp. 269 - 286
Copyright
2004 Cambridge Philosophical Society

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