A Littlewood–Richardson rule for Macdonald polynomials
نویسندگان
چکیده
منابع مشابه
Matrix product and sum rule for Macdonald polynomials
We present a new, explicit sum formula for symmetric Macdonald polynomials Pλ and show that they can be written as a trace over a product of (infinite dimensional) matrices. These matrices satisfy the Zamolodchikov– Faddeev (ZF) algebra. We construct solutions of the ZF algebra from a rank-reduced version of the Yang–Baxter algebra. As a corollary, we find that the normalization of the stationa...
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We introduce a polynomial C(mu)[Z; q, t], depending on a set of variables Z = z(1), z(2),..., a partition mu, and two extra parameters q, t. The definition of C(mu) involves a pair of statistics (maj(sigma, mu), inv(sigma, mu)) on words sigma of positive integers, and the coefficients of the z(i) are manifestly in N[q,t]. We conjecture that C(mu)[Z; q, t] is none other than the modified Macdona...
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Abstract. In this paper we use the combinatorics of alcove walks to give a uniform combinatorial formula for Macdonald polynomials for all Lie types. These formulas are generalizations of the formulas of Haglund-Haiman-Loehr for Macdonald polynoimals of type GLn. At q = 0 these formulas specialize to the formula of Schwer for the Macdonald spherical function in terms of positively folded alcove...
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In [LLT1], Lascoux, Leclerc and Thibon give some factorisation formulas for Hall-Littlewood functions when the parameter q is specialized at roots of unity. They also give formulas in terms of cyclic characters of the symmetric group. In this article, we give a generalization of these specializations for different versions of the Macdonald polynomials and we obtain similar formulas in terms of ...
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ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 2012
ISSN: 0025-5874,1432-1823
DOI: 10.1007/s00209-012-0986-z