Equivariant-trace realization of multi-t Macdonald polynomials for rectangular partitions

Establish that, for every rectangular partition, the multi-t Macdonald polynomials are obtained as equivariant traces of suitable Yang–Baxter elements of Hecke algebras.

Background

The paper introduces noncommutative and multi-t analogues of Macdonald polynomials and relates them to Yang–Baxter elements in Hecke algebras. For rectangular partitions, the authors observe that the relevant commutative specializations appear to agree with previously known multi-t Hall–Littlewood functions. This motivates the unresolved conjecture that the multi-t Macdonald polynomials admit an equivariant-trace realization through Yang–Baxter elements, linking symmetric-function identities with Hecke-algebra and quantum-group constructions.