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The Quarterly Journal of Mathematics Advance Access originally published online on May 29, 2007
The Quarterly Journal of Mathematics 2007 58(3):319-344; doi:10.1093/qmath/ham016
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© 2007. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

LANGLANDS DUALITY AND G2 SPECTRAL CURVES

Nigel Hitchin{dagger}

Mathematical Institute, 24-29 St Giles', Oxford OX1 3LB, UK

{dagger} E-mail: hitchin{at}maths.ox.ac.uk

Received 5 January 2007;
  Abstract

We first demonstrate how duality for the fibres of the so-called Hitchin fibration works for the Langlands dual groups Sp(2m) and SO(2m + 1). We then show that duality for G2 is implemented by an involution on the base space which takes one fibre to its dual. A formula for the natural cubic form is given and shown to be invariant under the involution.


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