A class of irreducible modules for the extended affine Lie algebra \(\widetilde{\mathfrak{gl}}_l(\mathbb{C}_q)\)

DOI10.1007/s11425-011-4166-0zbMath1293.17033arXiv0904.1045OpenAlexW2027118636WikidataQ115378218 ScholiaQ115378218MaRDI QIDQ657285

Zi Ting Zeng

Publication date: 16 January 2012

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0904.1045

zbMATH Keywords

irreducible modulesfree fieldsextended affine Lie algebra

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67)

Related Items (6)

Irreducible Wakimoto-like modules for the Lie superalgebra \(D(2, 1;\alpha)\) ⋮ A family of representations of the affine Lie superalgebra \(\widehat{\mathfrak{gl}}_{m | n}(\mathbb{C})\) ⋮ A family of representations of the Lie superalgebra \(\widehat{\mathfrak{gl}_{1|l-1}}(\mathbb C_q)\) ⋮ A family of representations of the Lie superalgebra \(\widehat{\mathfrak{gl}_{m | n}}(\mathbb{C}_q)\) ⋮ Localization of highest weight modules of a class of extended affine Lie algebras ⋮ Integral structures in extended affine Lie algebras

Cites Work

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• Unitary representations of the extended affine Lie algebra \(\widetilde{\mathfrak{gl}_3(\mathbb C_q})\).
• Fock representations of the affine Lie algebra \(A_ 1^{(1)}\)
• Double-loop algebras and the Fock space
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• Vertex operators arising from the homogeneous realization for \(\widehat{\text{gl}}_N\)
• A unified view of some vertex operator constructions
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• IRREDUCIBLE WAKIMOTO-LIKE MODULES FOR THE AFFINE LIE ALGEBRA $\widehat{\mathfrak{g}{\mathfrak{l}_n}}$
• Extended affine Lie algebras and their root systems
• Fermionic and Bosonic Representations of the Extended Affine Lie Algebra
• Unitary Modules for EALAs Co-ordinatized by a Quantum Torus
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