000			01791 a2200217 4500
005			20180924110139.0
008			180918b xxu||||| |||| 00| 0 eng d
020			_a9781470436599
040			_cIIT Kanpur
041			_aeng
082			_a512.482 _bM732s
100			_aMolev, Alexander
245			_aSugawara operators for classical lie algebras _cAlexander Molev
260			_bAmerican Mathematical Society _c2018 _aProvidence
300			_axiv, 304p
440			_aMathematical surveys and monographs; v.229
520			_aThe celebrated Schur-Weyl duality gives rise to effective ways of constructing invariant polynomials on the classical Lie algebras. The emergence of the theory of quantum groups in the 1980s brought up special matrix techniques which allowed one to extend these constructions beyond polynomial invariants and produce new families of Casimir elements for finite-dimensional Lie algebras. Sugawara operators are analogs of Casimir elements for the affine Kac-Moody algebras. The goal of this book is to describe algebraic structures associated with the affine Lie algebras, including affine vertex algebras, Yangians, and classical $\mathcal{W}$-algebras, which have numerous ties with many areas of mathematics and mathematical physics, including modular forms, conformal field theory, and soliton equations. An affine version of the matrix technique is developed and used to explain the elegant constructions of Sugawara operators, which appeared in the last decade. An affine analogue of the Harish-Chandra isomorphism connects the Sugawara operators with the classical $\mathcal{W}$-algebras, which play the role of the Weyl group invariants in the finite-dimensional theory.
650			_aLie algebras
650			_aAffine algebraic groups
942			_cBK
999			_c559274 _d559274