English

Diamond of triads

High Energy Physics - Theory 2025-12-19 v3 Mathematical Physics math.MP Quantum Algebra

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.

Cite

@article{arxiv.2503.07592,
  title  = {Diamond of triads},
  author = {A. Mironov and A. Morozov and A. Popolitov and Z. Zakirova},
  journal= {arXiv preprint arXiv:2503.07592},
  year   = {2025}
}

Comments

9 pages, LaTeX

R2 v1 2026-06-28T22:14:28.808Z