Mixed Tensor Representations of Quantum Superalgebra q(gl(m,n))

Shader, Chanyoung Lee; Moon, Dongho

doi:10.1080/00927870601115682

Cited by 3 publications

(4 citation statements)

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“…We let X M ,N m ,n denote the algebra of endomorphisms of U q s ℓpM |N q on mixed tensor product V ‹bm b V bn . As was shown in [71] (see also [50,51,49,52]) there is a surjective homomorphism…”

Section: Corollarymentioning

confidence: 59%

Bimodule structure of the mixed tensor product over $U_{q} s\ell(2|1)$ and quantum walled Brauer algebra

Bulgakova,

Kiselev,

Tipunin

2017

Preprint

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We study a mixed tensor product 3 3 3 bm b3 3 3 bn of the three-dimensional fundamental representations of the Hopf algebra U q s ℓp2|1q, whenever q is not a root of unity. Formulas for the decomposition of tensor products of any simple and projective U q s ℓp2|1q-module with the generating modules 3 3 3 and 3 3 3 are obtained. The centralizer of U q s ℓp2|1q on the mixed tensor product is calculated. It is shown to be the quotient X m,n of the quantum walled Brauer algebra qwB m,n . The structure of projective modules over X m,n is written down explicitly. It is known that the walled Brauer algebras form an infinite tower. We have calculated the corresponding restriction functors on simple and projective modules over X m,n . This result forms a crucial step in decomposition of the mixed tensor product as a bimodule over X m,n b U q s ℓp2|1q.We give an explicit bimodule structure for all m , n.

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Section: Corollarymentioning

confidence: 59%

Bimodule structure of the mixed tensor product over $U_{q} s\ell(2|1)$ and quantum walled Brauer algebra

Bulgakova,

Kiselev,

Tipunin

2017

Preprint

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“…By the definitions of F r,s (q) and BT r,s (q) and Theorem 4. 16, we obtain the following corollary.…”

Section: Letmentioning

confidence: 71%

“…By replacing gl(n) by the quantum enveloping algebra U q (gl(n)) and V = C n by V q = C(q) n , we obtain as the centralizer algebra the quantum walled Brauer algebra studied in [3,4,7,11,14]. Super versions of the above constructions have been investigated with the following substitutions: Replace gl(n) by gl(m|n), C n by C (m|n) ; U q (gl(n)) by U q (gl(m|n)); and C(q) n by C(q) (m|n) as in [15,16].…”

Section: Introductionmentioning

confidence: 99%

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Quantum walled Brauer–Clifford superalgebras

et al. 2016

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Abstract. We introduce a new family of superalgebras, the quantum walled Brauer-Clifford superalgebras BCr,s(q). The superalgebra BCr,s(q) is a quantum deformation of the walled BrauerClifford superalgebra BCr,s and a super version of the quantum walled Brauer algebra. We prove that BCr,s(q) is the centralizer superalgebra of the action of Uq(q(n)) on the mixed tensor space V r,s q⊗s when n ≥ r + s, where Vq = C(q) (n|n) is the natural representation of the quantum enveloping superalgebra Uq(q(n)) and V * q is its dual space. We also provide a diagrammatic realization of BCr,s(q) as the (r, s)-bead tangle algebra BTr,s(q). Finally, we define the notion of q-Schur superalgebras of type Q and establish their basic properties.

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