Symplectic leaves of \(W\)-algebras from the reduced Kac-Moody point of view. (English) Zbl 1062.81524

Mladenov, Ivaïlo M. (ed.) et al., Proceedings of the 2nd international conference on geometry, integrability and quantization, Varna, Bulgaria, June 7–15, 2000. Sofia: Coral Press Scientific Publishing (ISBN 954-90618-2-5/pbk). 99-109 (2001).
Summary: The symplectic leaves of \(W\)-algebras are the intersections of the symplectic leaves of the Kac-Moody algebras and the hypersurface of the second class constraints, which define the \(W\)-algebra. This viewpoint enables us to classify the symplectic leaves and also to give a representative for each of them. The case of the \(W_2\) (Virasoro) algebra is investigated in detail, where the positivity of the energy functional is also analyzed.
For the entire collection see [Zbl 0957.00038].


81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations
Full Text: arXiv