On the Connection Between Macdonald Polynomials and Demazure Characters

By Yasmine B. Sanderson. 2000

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Weyl modules and $$q$$q-Whittaker functions (2012, unknown): “All of our results are known for the polynomials Ψ ′ λ̌ (and thus, in particular, we can show that Ψ λ̌ = Ψ ′ λ̌ ) due to [5,18,20] but our proofs are totally different from [5,18,20].”
Nonsymmetric Macdonald polynomials and Demazure characters (2001, background): “Let us mention that in the An-case, as explained in [ Sa ], the positivity of the above coefficients is closely related to the positivity of the Kostka-Foulkes polynomials via the duality of the two variable Kostka functions.”
Refinements of the Littlewood-Richardson rule (2009, methodology): “By letting q = t = 0, we obtain a new combinatorial formula for the Eα(X; 0; 0), which are known (13) to be certain B-module characters studied by Demazure, now commonly referred to as Demazure characters.”
BGG reciprocity for current algebras (2011, background): “In particular, it is known that, for g twisted or simply laced untwisted and after a certain specialization of the parameters, nonsymmetric Macdonald polynomials are the Demazure characters for the level one highest weight grepresentations [19,32].”