Dual canonical bases for the quantum general linear supergroup
نویسندگان
چکیده
منابع مشابه
Dual Canonical Bases for the Quantum General Linear Supergroup
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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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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Abstract. A string basis is constructed for each subalgebra of invariants of the function algebra on the quantum special linear group. By analyzing the string basis for a particular subalgebra of invariants, we obtain a “canonical basis” for every finite dimensional irreducible Uq(sl(n))-module. It is also shown that the algebra of functions on any quantum homogeneous space is generated by quan...
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The dual basis of the canonical basis of the modified quantized enveloping algebra is studied, in particular for type A. The construction of a basis for the coordinate algebra of the n × n quantum matrices is appropriate for the study the multiplicative property. It is shown that this basis is invariant under multiplication by certain quantum minors including the quantum determinant. Then a bas...
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In this article we consider a generalization of Donkon-Koppinen filtrations for coordinate superalgebras of general linear supergroups. More precisely, if G = GL(m|n) is a general linear supergroup of (super)degree (m|n), then its coordinate superalgebra K[G] is a natural G × G-supermodule. For any finitely generated ideal Γ ⊆ Λ × Λ the largest supersubmodule OΓ(K[G]), whose all composition fac...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2006
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2005.11.023