METHODS OF PHYSICAL INVESTIGATION

Diamond of triads

A. Mironov^abc, A. Morozov^adb, A. Popolitov^adb, Z. Zakirova<sup>de

a</sup> National Research Center Kurchatov Institute, 123182, Moscow, Russia
^b Moscow Institute of Physics and Technology (National Research University), 141701, Dolgoprudny, Moscow region, Russia
^c Lebedev Physical Institute, Russian Academy of Sciences, 119991, Moscow, Russia
^d Institute for Information Transmission Problems, Russian Academy of Sciences, 127994, Moscow, Russia
^e Kazan State Power Engineering University, 420066, Kazan, Russia

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 Ding–Iohara–Miki algebras. This completes the list of polynomials associated with Seiberg–Witten theory with adjoint matter in various dimensions.

Received: 09.03.2025
Revised: 06.04.2025
Accepted: 06.04.2025

DOI: 10.31857/S0370274X25050127

 English version: Journal of Experimental and Theoretical Physics Letters, 2025, 121:9, 752–758