A Lie Algebra of Grassmannian Dirac Operators and Vector Variables

摘要

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.