A Lie algebra of Grassmannian Dirac operators and vector variables

2021/10/05 by Bisbo, Asmus K., De Bie, Hendrik, Van der Jeugt, Joris
#15A66 #15A75 (Secondary) #17B10 (Primary) 05E10 #81R05 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2110.02091

Abstract

The Lie algebra generated by m p-dimensional Grassmannian Dirac operators and m p-dimensional vector variables is identified as the orthogonal Lie algebra \mathfrakso(2m+1). In this paper, we study the space P of polynomials in these vector variables, corresponding to an irreducible \mathfrakso(2m+1) representation. In particular, a basis of P is constructed, using various Young tableaux techniques. Throughout the paper, we also indicate the relation to the theory of parafermions.

Related

• Models for irreducible representations of the symplectic algebra using Dirac-type operators
• Paragrassmann Algebras with Many Variables
• Symplectic Dirac operators for Lie algebras and graded Hecke algebras
• Orthogonal polynomials and Lie superalgebras
• The \mathfraksl₂-actions on the symmetric polynomials and on Young diagrams