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OverviewThe 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. Full Product DetailsAuthor: Alexander MolevPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.713kg ISBN: 9781470436599ISBN 10: 1470436590 Pages: 305 Publication Date: 28 February 2018 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsIdempotents and traces Invariants of symmetric algebras Manin matrices Casimir elements for $\mathfrak{gl}_N$ Casimir elements for $\mathfrak{o}_N$ and $\mathfrak{sp}_N$ Feigin-Frenkel center Generators in type $A$ Generators in types $B, C$ and $D$ Commutative subalgebras of $\textrm{U}(\mathfrak{g})$ Yangian characters in type $A$ Yangian characters in types $B, C$ and $D$ Classical $\mathcal{W}$-algebras Affine Harish-Chandra isomorphism Higher Hamiltonians in the Gaudin model Wakimoto modules Bibliography IndexReviewsAuthor InformationAlexander Molev, University of Sydney, Australia. Tab Content 6Author Website:Countries AvailableAll regions |
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