Structure and Representations of the Quantum General Linear Supergroup
نویسندگان
چکیده
منابع مشابه
Structure and Representations of the Quantum General Linear Supergroup
The structure and representations of the quantum general linear supergroup GLq(m|n) are studied systematically by investigating the Hopf superalgebra Gq of its representative functions. Gq is factorized into G π q G π̄ q , and a Peter Weyl basis is constructed for each factor. Parabolic induction for the quantum supergroup is developed. The underlying geometry of induced representations is discu...
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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 translati...
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15 صفحه اولGeometry and Representations of the Quantum Supergroup Osp
The quantum supergroup OSPq(1|2n) is studied systematically. A Haar functional is constructed, and an algebraic version of the Peter Weyl theory is extended to this quantum supergroup. Quantum homogeneous superspaces and quantum homogeneous supervector bundles are defined following the strategy of Connes’ theory. Parabolic induction is developed by employing the quantum homogeneous supervector ...
متن کاملGeometry of Quantum Homogeneous Supervector Bundles and Representation Theory of Quantum General Linear Supergroup
The quantum general linear supergroup GL q (m|n) is defined and its structure is studied systematically. Quantum homogeneous supervector bundles are introduced following Connes' theory, and applied to develop the representation theory of GL q (m|n). Quantum Frobenius reciprocity is proven, and a Borel-Weil theorem is established for the covariant and contravariant tensor irreps.
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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 1998
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s002200050401