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<p>The triad refers to embedding of two systems of polynomials, symmetric ones and those of the Baker–Akhiezer type into a power series of the Noumi–Shiraishi type. It provides an alternative definition of Macdonald theory and its extensions. The basic triad is associated with the vector representation of the Ding–Iohara–Miki (DIM) algebra. We discuss lifting this triad to two elliptic generalizations and further to the bi-elliptic triad. At the algebraic level, it corresponds to elliptic and bi-elliptic Ding–Iohara–Miki algebras. This co-mpletes the list of polynomials associated with Seiberg–Witten theory with adjoint matter in various dimensions.</p>

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Diamond of Triads

  • 期刊论文

  • 发表日期：

    2025年4月28日

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  • A. Mironov,
  • A. Morozov,
  • A. Popolitov,
  • Z. Zakirova

摘要

The triad refers to embedding of two systems of polynomials, symmetric ones and those of the Baker–Akhiezer type into a power series of the Noumi–Shiraishi type. It provides an alternative definition of Macdonald theory and its extensions. The basic triad is associated with the vector representation of the Ding–Iohara–Miki (DIM) algebra. We discuss lifting this triad to two elliptic generalizations and further to the bi-elliptic triad. At the algebraic level, it corresponds to elliptic and bi-elliptic Ding–Iohara–Miki algebras. This co-mpletes the list of polynomials associated with Seiberg–Witten theory with adjoint matter in various dimensions.