
Journal of Lie Theory 32 (2022), No. 3, 751770 Copyright Heldermann Verlag 2022 A Lie Algebra of Grassmannian Dirac Operators and Vector Variables Asmus K. Bisbo Dept. of Applied Mathematics, Computer Science and Statistics, Faculty of Sciences, Ghent University, Belgium asmus.bisbo@ugent.be Hendrik De Bie Dept. of Electronics and Information Systems, Faculty of Engineering and Architecture, Ghent University, Belgium hendrik.debie@ugent.be Joris Van der Jeugt Dept. of Applied Mathematics, Computer Science and Statistics, Faculty of Sciences, Ghent University, Belgium joris.vanderjeugt@ugent.be The Lie algebra generated by m pdimensional Grassmannian Dirac operators and m pdimensional vector variables is identified as the orthogonal Lie algebra so(2m+1). In this paper, we study the space P of polynomials in these vector variables, corresponding to an irreducible so(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. Keywords: Representation theory, Lie algebras, Young tableaux, Clifford analysis, Grassmann algebras, parafermions. MSC: 17B10, 05E10, 81R05, 15A66, 15A75. [ Fulltextpdf (183 KB)] for subscribers only. 