Dual Canonical Bases for the Quantum General Linear Supergroup
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چکیده
Dual 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 Oq(SLm|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.
منابع مشابه
ar X iv : q - a lg / 9 71 20 46 v 2 2 8 Se p 19 98 Web bases for sl ( 3 ) are not dual canonical
or its invariant space Inv(V1 ⊗ V2 ⊗ . . .⊗ Vn). The quantum group Uq(g) has representations and vector spaces of invariants which generalize these, and one can also study their bases, with or without the intention of specializing to q = 1. (For simplicity, we will usually consider Uq(g) as an algebra over C(q ), and we will only occassionally mention Z[q] as a ground ring.) Lusztig’s remarkabl...
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تاریخ انتشار 2005