Dual canonical bases for the quantum general linear supergroup

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dc.creatorZhang, Hechun
dc.creatorZhang, R. B.
dc.date2005-10-10
dc.date.accessioned2026-07-07T06:47:17Z
dc.date.available2026-07-07T06:47:17Z
dc.descriptionDual canonical bases of the quantum general linear supergroup are constructed which are invariant under the multiplication of the quantum Berezinian. By setting the quantum Berezinian to identity, we obtain dual canonical bases of the quantum special linear supergroup ${\s O}_q(SL_{m\mid n})$. We apply the canonical bases to study invariant subalgebras of the quantum supergroups under left and right translations. In the case $n=1$, it is shown that each invariant subalgebra is spanned by a part of the dual canonical bases. This in turn leads to dual canonical bases for any Kac module constructed by using an analogue of Borel-Weil theorem.
dc.description32 pages
dc.identifierhttps://arxiv.org/abs/math/0510186
dc.identifierhttp://arxiv.org/abs/math/0510186
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/103604
dc.subjectQuantum Algebra
dc.subjectRepresentation Theory
dc.subject17B37
dc.titleDual canonical bases for the quantum general linear supergroup
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