Equivariant-trace realization of all Macdonald polynomials

Establish that all ordinary Macdonald polynomials can be obtained as equivariant traces of suitable Yang–Baxter elements of Hecke algebras.

Background

Beyond the rectangular case, the paper proposes a broader realization of Macdonald polynomials using equivariant traces of Yang–Baxter elements in Hecke algebras. The conjecture extends the preceding rectangular-partition claim to the entire family of ordinary Macdonald polynomials and is presented as an unresolved structural connection between Macdonald theory and Hecke-algebra representations.