Osaka Journal of Mathematics

Some quotient algebras arising from the quantum toroidal algebra $U_{q}(\mathit{sl}_{n+1}(\mathcal{C}_{\gamma}))$ ($n\geq 2$)

Kei Miki

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Some quotient algebras arising from the quantum toroidal algebra $U_{q}(\mathit{sl}_{n+1}(\mathcal{C}_{\gamma}))$ ($n\ge 2$) are considered. They are related to integrable highest weight representations of the algebra and are shown to be isomorphic to tensor products of two algebras of symmetric Laurent polynomials and Macdonald's difference operators.

Article information

Osaka J. Math., Volume 43, Number 4 (2006), 895-922.

First available in Project Euclid: 11 December 2006

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Zentralblatt MATH identifier

Primary: 17B37: Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23]
Secondary: 17B67: Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras 33D52: Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.)


Miki, Kei. Some quotient algebras arising from the quantum toroidal algebra $U_{q}(\mathit{sl}_{n+1}(\mathcal{C}_{\gamma}))$ ($n\geq 2$). Osaka J. Math. 43 (2006), no. 4, 895--922.

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