Quantizing Mishchenko–Fomenko subalgebras for centralizers via affine $W$-algebras

DOI10.1090/mosc/264zbMath1441.17012arXiv1611.00852OpenAlexW2547925618MaRDI QIDQ4584300

Alexander Premet, Tomoyuki Arakawa

Publication date: 30 August 2018

Published in: Transactions of the Moscow Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.00852

zbMATH Keywords

vertex algebrasaffine \(W\)-algebrasMishchenko-Fomenko subalgebras

Mathematics Subject Classification ID

Universal enveloping (super)algebras (17B35) Vertex operators; vertex operator algebras and related structures (17B69) Simple, semisimple, reductive (super)algebras (17B20) Coadjoint orbits; nilpotent varieties (17B08)

Related Items

Takiff algebras with polynomial rings of symmetric invariants ⋮ The symmetric invariants of centralizers and Slodowy grading ⋮ On the fibres of Mishchenko-Fomenko systems ⋮ Center at the critical level for centralizers in type \(A\) ⋮ Casimir elements and Sugawara operators for Takiff algebras ⋮ Quantisation and nilpotent limits of Mishchenko–Fomenko subalgebras ⋮ Classical \(\mathcal{W}\)-algebras for centralizers ⋮ On integrability of transverse Lie-Poisson structures at nilpotent elements ⋮ A bi-Hamiltonian nature of the Gaudin algebras

Cites Work

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• Zhu's algebra, \(C_2\)-algebra and \(C_2\)-cofiniteness of parafermion vertex operator algebras
• Quantum reduction and representation theory of superconformal algebras
• The index of centralizers of elements of reductive Lie algebras
• A remark on the \(C_2\)-cofiniteness condition on vertex algebras
• Representation theory of superconformal algebras and the Kac-Roan-Wakimoto conjecture
• The argument shift method and the Gaudin model
• The symmetric invariants of centralizers and Slodowy grading
• The argument shift method and maximal commutative subalgebras of Poisson algebras
• A new interpretation of Gelfand-Tsetlin bases
• Quantum reduction for affine superalgebras
• Some amazing properties of spherical nilpotent orbits
• Bethe subalgebras in twisted Yangians
• A degree inequality for Lie algebras with a regular Poisson semi-center
• Limits of Gaudin algebras, quantization of bending flows, Jucys-Murphy elements and Gelfand-Tsetlin bases
• On symmetric invariants of centralisers in reductive Lie algebras
• Surprising properties of centralisers in classical Lie algebras
• Wakimoto modules, opers and the center at the critical level
• The quantum Gaudin system
• Abelianizing vertex algebras
• Gaudin models with irregular singularities
• On some commutative subalgebras of the universal enveloping algebra of the Lie algebra $ \mathfrak{gl}(n,\mathbb C)$
• Algebraic Groups and Quantum Groups
• INVARIANTS OF FINITE GROUP SCHEMES
• ON CERTAIN COMMUTATIVE SUBALGEBRAS OF A UNIVERSAL ENVELOPING ALGEBRA
• Associated Varieties of Modules Over Kac-Moody Algebras and C2-Cofiniteness of W-Algebras
• On Higher-Order Sugawara Operators
• Vertex algebras, Kac-Moody algebras, and the Monster
• AFFINE KAC-MOODY ALGEBRAS AT THE CRITICAL LEVEL AND GELFAND-DIKII ALGEBRAS
• Modular invariance of characters of vertex operator algebras
• Lie Group Representations on Polynomial Rings