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Title: Hirota equations associated with simply laced affine Lie algebras: The cuspidal class E{sub 6} of e{sub 6}{sup (1)}

In this paper we derive Hirota equations associated with the simply laced affine Lie algebras g{sup (1)}, where g is one of the simply laced complex Lie algebras a{sub n},d{sub n},e{sub 6},e{sub 7} or e{sub 8}, defined by finite order automorphisms of g which we call Lepowsky automorphisms. In particular, we investigate the Hirota equations for Lepowsky automorphisms of e{sub 6} defined by the cuspidal class E{sub 6} of the Weyl group W(E{sub 6}) of e{sub 6}. We also investigate the relationship between the Lepowsky automorphisms of the simply laced complex Lie algebras g and the conjugate canonical automorphisms defined by Kac. This analysis is applied to identify the canonical automorphisms for the cuspidal class E{sub 6} of e{sub 6}.
Authors:
 [1]
  1. Mathematical Institute, University of Oxford, Woodstock Road, Oxford OX2 6HD (United Kingdom)
Publication Date:
OSTI Identifier:
22251279
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 2; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; EQUATIONS; LIE GROUPS