Sugawara operators for classical Lie algebras /
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| Author / Creator: | Molev, Alexander, 1961- author. |
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| Imprint: | Providence, Rhode Island : American Mathematical Society, [2018] |
| Description: | xiv, 304 pages : illustrations ; 26 cm. |
| Language: | English |
| Series: | Mathematical surveys and monographs ; volume 229 Mathematical surveys and monographs ; no. 229. |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11454588 |
| Summary: | The 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.<br> <br> 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. |
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| Physical Description: | xiv, 304 pages : illustrations ; 26 cm. |
| Bibliography: | Includes bibliographical references (pages 295-302) and index. |
| ISBN: | 9781470436599 1470436590 |