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ЖУРНАЛЫ // Symmetry, Integrability and Geometry: Methods and Applications // Архив

SIGMA, 2021, том 17, 031, 27 стр. (Mi sigma1714)

Эта публикация цитируется в 2 статьях

Representations of the Lie Superalgebra $\mathfrak{osp}(1|2n)$ with Polynomial Bases

Asmus K. Bisbo, Hendrik De Bie, Joris Van der Jeugt

Ghent University, B-9000 Gent, Belgium

Аннотация: We study a particular class of infinite-dimensional representations of $\mathfrak{osp}(1|2n)$. 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 $\mathfrak{osp}(1|2n)$. We construct a new polynomial basis for $L_n(p)$ arising from the embedding $\mathfrak{osp}(1|2np) \supset \mathfrak{osp}(1|2n)$. 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 $\mathfrak{osp}(1|2n)$ on these basis vectors requires further combinatorics, such as the action of a Young subgroup on the horizontal strips of the tableau.

Ключевые слова: representation theory, Lie superalgebras, Young tableaux, Clifford analysis, parabosons.

MSC: 17B10, 05E10, 81R05, 15A66

Поступила: 30 июня 2020 г.; в окончательном варианте 10 марта 2021 г.; опубликована 25 марта 2021 г.

Язык публикации: английский

DOI: 10.3842/SIGMA.2021.031



Реферативные базы данных:
ArXiv: 1912.06488


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