On higher order Sugawara operators

Details On higher order Sugawara operators On higher order Sugawara operators

2008-08-14

arxiv.org/abs/0808.1947v2

IMRN, 2009, no.9, 1612-1635.

Mathematics

Representation Theory

20 pages, some corrections are made, references added

Scientific paper

10.1093/imrn/rnn168

The higher Sugawara operators acting on the Verma modules over the affine Kac-Moody algebra at the critical level are related to the higher Hamiltonians of the Gaudin model due to work of Feigin, Frenkel and Reshetikhin. An explicit construction of the higher Hamiltonians in the case of gl_n was given recently by Talalaev. We propose a new approach to these results from the viewpoint of the vertex algebra theory by proving directly the formulas for the higher order Sugawara operators. The eigenvalues of the operators in the Wakimoto modules of critical level are also calculated.

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