Specializations of Macdonald Polynomials

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Macdonald often included in his talks the “specialization square” for symmetric Macdonald polynomials, which has monomial symmetric functions on the top edge, elementary symmetric functions on the right edge, Hall-Littlewood polynomials on the left edge, Schur functions on the diagonal and Jack polynomials in the upper right corner. This talk will explore the analogous “specialization square” for non-symmetric Macdonald polynomials. The primary tools are the monomial expansion formulas, the E-expansion formula, and the creation formula.