AFFINE KAC-MOODY ALGEBRAS AT THE CRITICAL LEVEL AND GELFAND-DIKII ALGEBRAS
- 1 April 1992
- journal article
- research article
- Published by World Scientific Pub Co Pte Ltd in International Journal of Modern Physics A
- Vol. 07 (supp01a) , 197-215
- https://doi.org/10.1142/s0217751x92003781
Abstract
We prove Drinfeld's conjecture that the center of a certain completion of the universal enveloping algebra of an affine Kac-Moody algebra at the critical level is isomorphic to the Gelfand-Dikii algebra, associated to the Langlands dual algebra. The center is identified with a limit of the W-algebra, defined by means of the quantum Drinfeld-Sokolov reduction.Keywords
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