Abstract
We give a direct proof of the combinatorial formula for interpolation Macdonald polynomials by introducing certain polynomials, which we call generic Macdonald polynomials, and which depend on d additional parameters and specialize to all Macdonald polynomials of degree d. The form of these generic polynomials is that of a Bethe eigenfunction and they imitate, on a more elementary level, the R-matrix construction of quantum immanants.
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Okounkov, A. Combinatorial formula for Macdonald polynomials and generic Macdonald polynomials. Transformation Groups 8, 293–305 (2003). https://doi.org/10.1007/s00031-003-0306-0
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DOI: https://doi.org/10.1007/s00031-003-0306-0