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Elliptic Ding-Iohara Algebra and the Free Field Realization of the Elliptic Macdonald Operator

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arxiv 1301.4912 v6 pith:G54WGQI4 submitted 2013-01-21 math.QA

Yosuke Saito This is my paper · ORCID
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keywords ellipticalgebrading-ioharafieldfreemacdonaldoperatorrealization
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The Ding-Iohara algebra is a quantum algebra arising from the free field realization of the Macdonald operator. Starting from the elliptic kernel function introduced by Komori, Noumi and Shiraishi, we can define an elliptic analog of the Ding-Iohara algebra. The free field realization of the elliptic Macdonald operator is also constructed.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A basic triad in Macdonald theory

    hep-th 2024-11 conditional novelty 6.0 of 10

    At t=q^{-m}, the Noumi-Shiraishi series reproduces the Baker-Akhiezer function, completing a triad with the Macdonald polynomials.

  2. Elliptic triad

    hep-th 2024-12 conditional novelty 4.0 of 10

    The paper argues that the Macdonald triad admits elliptic deformations, but the defining linear equations for elliptic Baker-Akhiezer functions remain ambiguous except at m=1.

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