Macdonald Polynomials and level two Demazure modules for affine \mathfraksl_n+1

2019/10/13 by Rekha Biswal, Biswal, Rekha, Vyjayanthi Chari +5
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1910.05848

openalex publication_date 2019/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define a family of symmetric polynomials G_ν,λ(z₁,⋯, z_n+1,q) indexed by a pair of dominant integral weights. The polynomial G_ν,0(z,q) is the specialized Macdonald polynomial and we prove that G_0,λ(z,q) is the graded character of a level two Demazure module associated to the affine Lie algebra \widehat\mathfraksl_n+1. Under suitable conditions on (ν,λ) (which includes the case when ν=0 or λ=0) we prove that G_ν,λ(z,q) is Schur positive and give explicit formulae for them in terms of Macdonald polynomials.

Citations

• BGG reciprocity for current algebras

Related

• Nonsymmetric Macdonald polynomials and Demazure characters
• Demazure submodules of level-zero extremal weight modules and specializations of Macdonald polynomials
• Specialization of nonsymmetric Macdonald polynomials at t=∞ and Demazure submodules of level-zero extremal weight modules
• Highest weight categories and Macdonald polynomials
• Demazure crystals for specialized nonsymmetric Macdonald polynomials