Some Properties of Macdonald Polynomials with Prescribed Symmetry

2010/01/18 by W. Baratta, Baratta, W.
Mathematics · #81Q08 #81V08 #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #msc:81Q08 #msc:81V08

paper · pdf · doi:10.48550/arxiv.1001.3134

21 Pages

arxiv created 2010/01/18 · arxiv updated 2010/02/26

Abstract

The Macdonald polynomials with prescribed symmetry are obtained from the nonsymmetric Macdonald polynomials via the operations of t-symmetrisation, t-antisymmetrisation and normalisation. Motivated by corresponding results in Jack polynomial theory we proceed to derive an expansion formula and a related normalisation. Eigenoperator methods are used to relate the symmetric and antisymmetric Macdonald polynomials, and we discuss how these methods can be extended to special classes of the prescribed symmetry polynomials in terms of their symmetric counterpart. We compute the explicit form of the normalisation with respect to the constant term inner product. Surpassing our original motivation, this is used to provide a derivation of a special case of a conjectured q-constant term identity.

Related

• Symmetric and non-symmetric Macdonald polynomials
• A new derivation of the inner product formula for the Macdonald symmetric polynomials
• The m-symmetric Macdonald polynomials
• Representation-theoretic proof of the inner product and symmetry identities for MacDonald's polynomials
• Compact formulas for Macdonald polynomials and quasisymmetric Macdonald polynomials