Sugawara Operators for Classical Lie Algebras

DOI10.1090/surv/229zbMath1395.17001OpenAlexW2924713230MaRDI QIDQ4637463

Alexander I. Molev

Publication date: 19 April 2018

Published in: Mathematical Surveys and Monographs (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/surv/229

zbMATH Keywords

Brauer algebraHamiltonianidempotentcentertraceLie algebraBethe ansatzsymmetric groupinvariantdeterminantSchur-Weyl dualityquantum algebravertex algebraCasimir elementYangianfree field realizationimmanantHarish-Chandra isomorphismManin matrixvacuum moduleSugawara operators

Mathematics Subject Classification ID

Universal enveloping (super)algebras (17B35) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Vertex operators; vertex operator algebras and related structures (17B69) Poisson algebras (17B63) Research exposition (monographs, survey articles) pertaining to nonassociative rings and algebras (17-02) Universal enveloping algebras of Lie algebras (16S30)

Related Items (16)

Gaudin models and multipoint conformal blocks: general theory ⋮ Hypergeometric sheaves for classical groups via geometric Langlands ⋮ Manin matrices of type \(C\): multi-parametric deformation ⋮ Symmetrisation and the Feigin–Frenkel centre ⋮ Minor identities for Sklyanin determinants ⋮ Subregular W-algebras of type A ⋮ Classical Whittaker modules for the classical affine Kac-Moody algebras ⋮ Center at the critical level for centralizers in type \(A\) ⋮ On Segal-Sugawara vectors and Casimir elements for classical Lie algebras ⋮ Casimir elements and Sugawara operators for Takiff algebras ⋮ Manin matrices for quadratic algebras ⋮ \(h\)-adic quantum vertex algebras associated with rational \(R\)-matrix in types \(B\), \(C\) and \(D\) ⋮ Split Casimir operator for simple Lie algebras, solutions of Yang–Baxter equations, and Vogel parameters ⋮ Strong generators of the subregular \(\mathcal{W}\)-algebra \(\mathcal{W}^{K-N}(\mathfrak{sl}_N, f_{\text{sub}})\) and combinatorial description at critical level ⋮ Quantisation and nilpotent limits of Mishchenko–Fomenko subalgebras ⋮ Higher-order Hamiltonians for the trigonometric Gaudin model

This page was built for publication: Sugawara Operators for Classical Lie Algebras