Representations of the Lie Superalgebra (1|2n) with Polynomial Bases
We study a particular class of infinite-dimensional representations of (1|2). These representations ₙ() are characterized by a positive integer p, and are the lowest component in the p-fold tensor product of the metaplectic representation of (1|2). We construct a new polynomial basis for ₙ() arising...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2021 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2021
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211318 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Representations of the Lie Superalgebra (1|2) with Polynomial Bases. Asmus K. Bisbo, Hendrik De Bie and Joris Van der Jeugt. SIGMA 17 (2021), 031, 27 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | We study a particular class of infinite-dimensional representations of (1|2). These representations ₙ() are characterized by a positive integer p, and are the lowest component in the p-fold tensor product of the metaplectic representation of (1|2). We construct a new polynomial basis for ₙ() arising from the embedding (1|2) ⊃ (1|2). The basis vectors of ₙ() are labelled by semi-standard Young tableaux, and are expressed as Clifford algebra-valued polynomials with integer coefficients in variables. Using combinatorial properties of these tableau vectors, it is deduced that they form a basis. The computation of matrix elements of a set of generators of (1|2) on these basis vectors requires further combinatorics, such as the action of a Young subgroup on the horizontal strips of the tableau.
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| ISSN: | 1815-0659 |