Symmetric and nonsymmetric Macdonald polynomials
نویسندگان
چکیده
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...
متن کاملThe binomial formula for nonsymmetric Macdonald polynomials
The q-binomial theorem is essentially the expansion of (x − 1)(x − q) · · · (x − q) in terms of the monomials x. In a recent paper [O], A. Okounkov has proved a beautiful multivariate generalization of this in the context of symmetric Macdonald polynomials [M1]. These polynomials have nonsymmetric counterparts [M2] which are of substantial interest, and in this paper we establish nonsymmetric a...
متن کاملSymmetric Functions and Macdonald Polynomials
The ring of symmetric functions Λ, with natural basis given by the Schur functions, arise in many different areas of mathematics. For example, as the cohomology ring of the grassmanian, and as the representation ring of the symmetric group. One may define a coproduct on Λ by the plethystic addition on alphabets. In this way the ring of symmetric functions becomes a Hopf algebra. The Littlewood–...
متن کاملSymmetric and Non-symmetric Macdonald Polynomials
The symmetric Macdonald polynomials are able to be constructed out of the non-symmetric Macdonald polynomials. This allows us to develop the theory of the symmetric Macdonald polynomials by first developing the theory of their non-symmetric counterparts. In taking this approach we are able to obtain new results as well as simpler and more accessible derivations of some of the known fundamental ...
متن کاملNonsymmetric Macdonald Polynomials and Matrix Coefficients for Unramified Principal Series
We show how a certain limit of the nonsymmetric Macdonald polynomials appears in the representation theory of semisimple groups over p–adic fields as matrix coefficients for the unramified principal series representations. The result is the nonsymmetric counterpart of a classical result relating the same limit of the symmetric Macdonald polynomials to zonal spherical functions on groups of p–ad...
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ژورنال
عنوان ژورنال: Annals of Combinatorics
سال: 1999
ISSN: 0218-0006,0219-3094
DOI: 10.1007/bf01608794