Crystal bases for the quantum queer superalgebra
In this paper, we develop the crystal basis theory for the quantum queer superalgebra $U_q(\mathfrak{q}(n))$. We define the notion of crystal bases and prove the tensor product rule for $U_q(\mathfrak{q}(n))$-modules in the category $\mathcal{O}^{\ge0}_{\mathrm {int}}$. Our main theorem shows that e...
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Veröffentlicht in: | Journal of the European Mathematical Society : JEMS 2015-01, Vol.17 (7), p.1593-1627 |
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Hauptverfasser: | , , , , |
Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | In this paper, we develop the crystal basis theory for the quantum queer superalgebra $U_q(\mathfrak{q}(n))$. We define the notion of crystal bases and prove the tensor product rule for $U_q(\mathfrak{q}(n))$-modules in the category $\mathcal{O}^{\ge0}_{\mathrm {int}}$. Our main theorem shows that every $U_q(\mathfrak{q}(n))$-module in the category $\mathcal{O}^{\ge0}_{\mathrm {int}}$ has a unique crystal basis. |
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ISSN: | 1435-9855 1435-9863 |
DOI: | 10.4171/JEMS/540 |