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arXiv · 2503.07592

Diamond of triads

A. Mironov·A. Morozov·A. Popolitov·Z. Zakirova
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Abstract

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 DIM algebras. This completes the list of polynomials associated with Seiberg-Witten theory with adjoint matter in various dimensions.

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A. Mironov, A. Morozov, A. Popolitov, Z. Zakirova. 2025-03-10. Diamond of triads. https://doi.org/10.1134/s002136402560586x

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