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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Abstract

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

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

Dates
First available in Project Euclid: 11 December 2006

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1165850041

Mathematical Reviews number (MathSciNet)
MR2303555

Zentralblatt MATH identifier
1136.17305

Subjects
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.)

Citation

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. https://projecteuclid.org/euclid.ojm/1165850041


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