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Representations of the Lie superalgebra osp(1 vertical bar 2n) with polynomial bases

Journal Contribution - Journal Article

We study a particular class of infinite-dimensional representations of osp(1 vertical bar 2n). These representations L-n(p) are characterized by a positive integer p, and are the lowest component in the p-fold tensor product of the metaplectic representation of osp(1 vertical bar 2n). We construct a new polynomial basis for L-n (p) arising from the embedding osp(1 vertical bar 2np) superset of osp(1 vertical bar 2n). The basis vectors of L-n(p) are labelled by semi-standard Young tableaux, and are expressed as Clifford algebra valued polynomials with integer coefficients in np variables. Using combinatorial properties of these tableau vectors it is deduced that they form indeed a basis. The computation of matrix elements of a set of generators of osp(1 vertical bar 2n) on these basis vectors requires further combinatorics, such as the action of a Young subgroup on the horizontal strips of the tableau.
Journal: SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS
ISSN: 1815-0659
Volume: 17
Publication year:2021
Accessibility:Open