Journal of Lie Theory

no. 3
A Lie Algebra of Grassmannian Dirac Operators and Vector Variables
Journal of Lie Theory, Volume 32 (2022) no. 3, pp. 751-770
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.
DOI: 10.5802/jolt.1250
Classification: 17B10, 05E10, 81R05, 15A66, 15A75
Keywords: Representation theory, Lie algebras, Young tableaux, Clifford analysis, Grassmann algebras, parafermions 
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     author = {A. K. Bisbo and H. De Bie and J. 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},
     doi = {10.5802/jolt.1250},
     zbl = {1507.17011},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1250/}
}
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A. K. Bisbo; H. De Bie; J. Van der Jeugt. A Lie Algebra of Grassmannian Dirac Operators and Vector Variables. Journal of Lie Theory, Volume 32 (2022) no. 3, pp. 751-770. doi: 10.5802/jolt.1250

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