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
Hauptverfasser: Grantcharov, Dimitar, Jung, Ji Hye, Kang, Seok-Jin, Kashiwara, Masaki, Kim, Myungho
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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.
ISSN:1435-9855
1435-9863
DOI:10.4171/JEMS/540