Abstracts

Asmus Bisbo

Polynomial representations of the Lie superalgebra osp(1|2n)

The well-studied boson Fock representation of osp(1|2n) can be easily realized in terms of partial derivatives and variable multiplications on the space of n-variable complex valued polynomials. Generalizing this situation by substituting the partial derivatives with p-dimensional Dirac operators and the variable multiplications with corresponding Clifford operators acting on spinor-valued polynomials, we get realizations of the paraboson representations of osp(1|2n) with lowest weight (p/2,...,p/2). Using a nice description of the characters of these representations in terms of Schur functions, we find concrete natural bases of Clifford algebra-valued polynomials indexed by semi-standard Young tableaux.