On the Connection Between Macdonald Polynomials and Demazure Characters
نویسنده
چکیده
We show that the specialization of nonsymmetric Macdonald polynomials at t = 0 are, up to multiplication by a simple factor, characters of Demazure modules for ŝl(n). This connection furnishes Lie-theoretic proofs of the nonnegativity and monotonicity of Kostka polynomials.
منابع مشابه
Nonsymmetric Macdonald Polynomials and Demazure Characters
We establish a connection between a specialization of the nonsymmetric Macdonald polynomials and the Demazure characters of the corresponding affine Kac-Moody algebra. This allows us to obtain a representation-theoretical interpretation of the coefficients of the expansion of the specialized symmetric Macdonald polynomials in the basis formed by the irreducible characters of the associated fini...
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Demazure characters can be decomposed into smaller pieces, called standard bases by Lascoux and Schützenberger. We prove that these polynomials, which we call Demazure atoms, are the same polynomials obtained from a certain specialization of nonsymmetric Macdonald polynomials. This combinatorial interpretation for Demazure atoms accelerates the computation of the key associated to a given semi-...
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It is an open problem to prove the Schubert positivity property combinatorially. Recently Haglund, Mason, Remmel, van Willigenburg et al. have studied the skyline fillings (a tableau-combinatorial object giving a combinatorial description to nonsymmetric MacDonald polynomials , proved by Haglund, Haiman and Loehr) specifically for the case of Demazure atoms (atoms) and key polynomials (keys). T...
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Demazure characters of type A, which are equivalent to key polynomials, have been decomposed by Lascoux and Schützenberger into standard bases. We prove that the resulting polynomials, which we call Demazure atoms, can be obtained from a certain specialization of nonsymmetric Macdonald polynomials. This combinatorial interpretation for Demazure atoms accelerates the computation of the right key...
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In the prequel to this paper [5], we showed how results of Mason [11], [12] involving a new combinatorial formula for polynomials that are now known as Demazure atoms (characters of quotients of Demazure modules, called standard bases by Lascoux and Schützenberger [6]) could be used to define a new basis for the ring of quasisymmetric functions we call “Quasisymmetric Schur functions” (QS funct...
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