Geodesic
A Lie Algebra of Grassmannian Dirac Operators and Vector Variables
Asmus K. Bisbo1 ; Hendrik De Bie2 ; Joris Van der Jeugt1
1Dept. of Applied Mathematics, Computer Science and Statistics, Faculty of Sciences, Ghent University, Belgium
2Dept. of Electronics and Information Systems, Faculty of Engineering and Architecture, Ghent University, Belgium
Journal of Lie Theory, Tome 32 (2022) no. 3, pp. 751-770

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 17B10, 05E10, 81R05, 15A66, 15A75
Mots-clés : Representation theory, Lie algebras, Young tableaux, Clifford analysis, Grassmann algebras, parafermions

Asmus K. Bisbo  1   ; Hendrik De Bie  2   ; Joris Van der Jeugt  1

1 Dept. of Applied Mathematics, Computer Science and Statistics, Faculty of Sciences, Ghent University, Belgium
2 Dept. of Electronics and Information Systems, Faculty of Engineering and Architecture, Ghent University, Belgium 
Asmus K. Bisbo; Hendrik De Bie; Joris Van der Jeugt. A Lie Algebra of Grassmannian Dirac Operators and Vector Variables. Journal of Lie Theory, Tome 32 (2022) no. 3, pp. 751-770. http://geodesic.mathdoc.fr/item/JOLT_2022_32_3_a6/
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     author = {Asmus K. Bisbo and Hendrik De Bie and Joris Van der Jeugt},
     title = {A {Lie} {Algebra} of {Grassmannian} {Dirac} {Operators} and {Vector} {Variables}},
     journal = {Journal of Lie Theory},
     pages = {751--770},
     year = {2022},
     volume = {32},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2022_32_3_a6/}
}
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