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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2021 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2021
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| Онлайн доступ: | 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 |
| Цитувати: | 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 |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862717638697811968 |
|---|---|
| author | Bisbo, Asmus K. De Bie, Hendrik Van der Jeugt, Joris |
| author_facet | Bisbo, Asmus K. De Bie, Hendrik Van der Jeugt, Joris |
| citation_txt | 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 |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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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| first_indexed | 2026-03-20T17:41:18Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211318 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-20T17:41:18Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Bisbo, Asmus K. De Bie, Hendrik Van der Jeugt, Joris 2025-12-29T11:10:16Z 2021 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 1815-0659 2020 Mathematics Subject Classification: 17B10; 05E10; 81R05; 15A66 arXiv:1912.06488 https://nasplib.isofts.kiev.ua/handle/123456789/211318 https://doi.org/10.3842/SIGMA.2021.031 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. The authors were supported by the EOS Research Project 30889451. The editor and referees are thanked for their helpful reports. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Representations of the Lie Superalgebra (1|2n) with Polynomial Bases Article published earlier |
| spellingShingle | Representations of the Lie Superalgebra (1|2n) with Polynomial Bases Bisbo, Asmus K. De Bie, Hendrik Van der Jeugt, Joris |
| title | Representations of the Lie Superalgebra (1|2n) with Polynomial Bases |
| title_full | Representations of the Lie Superalgebra (1|2n) with Polynomial Bases |
| title_fullStr | Representations of the Lie Superalgebra (1|2n) with Polynomial Bases |
| title_full_unstemmed | Representations of the Lie Superalgebra (1|2n) with Polynomial Bases |
| title_short | Representations of the Lie Superalgebra (1|2n) with Polynomial Bases |
| title_sort | representations of the lie superalgebra (1|2n) with polynomial bases |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211318 |
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