Weyl modules for mathfrakosp(1,2) and nonsymmetric Macdonald\n polynomials

2015/07/06 by Evgeny Feigin, Feigin, Evgeny, Ievgen Makedonskyi +1
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #Advanced Combinatorial Mathematics

paper · pdf · doi:10.48550/arxiv.1507.01362

Abstract

The main goal of our paper is to establish a connection between the Weyl\nmodules of the current Lie superalgebras (twisted and untwisted) attached to\n mathfrakosp(1,2) and the nonsymmetric Macdonald polynomials of types\nA₂⁽²⁾ and A₂^(2)\†. We compute the dimensions and construct\nbases of the Weyl modules. We also derive explicit formulas for the t=0 and\nt=\∞ specializations of the nonsymmetric Macdonald polynomials. We show\nthat the specializations can be described in terms of the Lie superalgebras\naction on the Weyl modules.\n

Related

• Generalized Weyl modules, alcove paths and Macdonald polynomials
• Generalized Weyl modules for twisted current algebras
• Highest weight categories and Macdonald polynomials
• Specialization of nonsymmetric Macdonald polynomials at t=∞ and Demazure submodules of level-zero extremal weight modules
• Representation theoretic realization of non-symmetric Macdonald polynomials at infinity