Journal of Lie Theory 32 (2022), No. 3, 751--770
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 p-dimensional Grassmannian Dirac operators and m p-dimensional 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.
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