Feigin, Boris; Frenkel, Edward Affine Kac-Moody algebras at the critical level and Gelfand-Dikii algebras. (English) Zbl 0925.17022 Int. J. Mod. Phys. A 7, Suppl. 1A, 197-215 (1992). Summary: 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-Solokov reduction. Cited in 4 ReviewsCited in 126 Documents MSC: 17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras 17B37 Quantum groups (quantized enveloping algebras) and related deformations PDFBibTeX XMLCite \textit{B. Feigin} and \textit{E. Frenkel}, Int. J. Mod. Phys. A 7, 197--215 (1992; Zbl 0925.17022) Full Text: DOI