School and Conference on Modern Mathematical Physics

9 - 14 September 2019, Belgrade, Serbia


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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.


Institute of Physics Belgrade (University of Belgrade)
Belgrade, Serbia
Faculty of Mathematics (University of Belgrade)
Belgrade, Serbia
Mathematical Institute (Serbian Academy of Sciences and Arts)
Belgrade, Serbia
Faculty of Science (University of Kragujevac)
Kragujevac, Serbia
Serbian Academy of Sciences and Arts (SASA)
Belgrade, Serbia


Institute of Nuclear Sciences "VinĨa" (University of Belgrade)
Belgrade, Serbia
Institute of Physics (University of Kragujevac)
Kragujevac, Serbia
Faculty of Physics (University of Belgrade)
Belgrade, Serbia
Faculty of Sciences (University of Novi Sad)
Novi Sad, Serbia
School of Electrical Engineering (University of Belgrade)
Belgrade, Serbia
SEENET-MTP (Southeastern European Network in Mathematical and Theoretical Physics)
Nis, Serbia