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D.v. Bulgakova - One of the best experts on this subject based on the ideXlab platform.
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bimodule structure of the Mixed Tensor product over uqsl 2 1 and quantum walled brauer algebra
Nuclear Physics, 2018Co-Authors: D.v. Bulgakova, A.m. Kiselev, Yu I TipuninAbstract:Abstract We study a Mixed Tensor product 3 ⊗ m ⊗ 3 ‾ ⊗ n of the three-dimensional fundamental representations of the Hopf algebra U q s l ( 2 | 1 ) , whenever q is not a root of unity. Formulas for the decomposition of Tensor products of any simple and projective U q s l ( 2 | 1 ) -module with the generating modules 3 and 3 ‾ are obtained. The centralizer of U q s l ( 2 | 1 ) on the Mixed Tensor product is calculated. It is shown to be the quotient X m , n of the quantum walled Brauer algebra qw B 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 ⊠ U q s l ( 2 | 1 ) . We give an explicit bimodule structure for all m , n .
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Bimodule structure of the Mixed Tensor product over Uqsℓ(2|1) and quantum walled Brauer algebra
Nuclear Physics B, 2018Co-Authors: D.v. Bulgakova, A.m. Kiselev, I. Yu. TipuninAbstract:Abstract We study a Mixed Tensor product 3 ⊗ m ⊗ 3 ‾ ⊗ n of the three-dimensional fundamental representations of the Hopf algebra U q s l ( 2 | 1 ) , whenever q is not a root of unity. Formulas for the decomposition of Tensor products of any simple and projective U q s l ( 2 | 1 ) -module with the generating modules 3 and 3 ‾ are obtained. The centralizer of U q s l ( 2 | 1 ) on the Mixed Tensor product is calculated. It is shown to be the quotient X m , n of the quantum walled Brauer algebra qw B 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 ⊠ U q s l ( 2 | 1 ) . We give an explicit bimodule structure for all m , n .
Hebing Rui - One of the best experts on this subject based on the ideXlab platform.
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Mixed Schur-Weyl duality between general linear Lie algebras and cyclotomic walled Brauer algebras
arXiv: Quantum Algebra, 2015Co-Authors: Hebing Rui, Linliang SongAbstract:Motivated by Brundan-Kleshchev's work on higher Schur-Weyl duality, we establish Mixed Schur-Weyl duality between general linear Lie algebras and cyclotomic walled Brauer algebras in an arbitrary level. Using weakly cellular bases of cyclotomic walled Brauer algebras, we classify highest weight vectors of certain Mixed Tensor modules of general linear Lie algebras. This leads to an efficient way to compute decomposition matrices of cyclotomic walled Brauer algebras arising from Mixed Schur-Weyl duality, which generalizes early results on level two walled Brauer algebras.
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HIGHEST WEIGHT VECTORS OF Mixed Tensor PRODUCTS OF GENERAL LINEAR LIE SUPERALGEBRAS
Transformation Groups, 2015Co-Authors: Hebing RuiAbstract:In this paper, a notion of cyclotomic (or level k) walled Brauer algebras ℬk, r, t is introduced for arbitrary positive integer k. It is proven that ℬk, r, t is free over a commutative ring with rank kr + t(r + t) ! if and only if it is admissible. Using super Schur-Weyl duality between general linear Lie superalgebras \( \mathfrak{g}{\mathfrak{l}}_{m\left|n\right.} \) and ℬ2, r, t, we give a classification of highest weight vectors of \( \mathfrak{g}{\mathfrak{l}}_{m\left|n\right.} \) -modules Mpqrt, the Tensor products of Kac-modules with Mixed Tensor products of the natural module and its dual. This enables us to establish an explicit relationship between \( \mathfrak{g}{\mathfrak{l}}_{m\left|n\right.} \) -Kac-modules and right cell (or standard) ℬ2, r, t-modules over C. Further, we find an explicit relationship between indecomposable tilting \( \mathfrak{g}{\mathfrak{l}}_{m\left|n\right.} \) -modules appearing in Mpqrt, and principal indecomposable right ℬ2, r, t-modules via the notion of Kleshchev bipartitions. As an application, decomposition numbers of ℬ2, r, t arising from super Schur-Weyl duality are determined.
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Affine walled Brauer algebras and super Schur–Weyl duality
Advances in Mathematics, 2015Co-Authors: Hebing RuiAbstract:Abstract A new class of associative algebras referred to as affine walled Brauer algebras are introduced. These algebras are free with infinite rank over a commutative ring containing 1. Then level two walled Brauer algebras over C are defined, which are some cyclotomic quotients of affine walled Brauer algebras. We establish a super Schur–Weyl duality between affine walled Brauer algebras and general linear Lie superalgebras, and realize level two walled Brauer algebras as endomorphism algebras of Tensor modules of Kac modules with Mixed Tensor products of the natural module and its dual over general linear Lie superalgebras, under some conditions. We also prove the weakly cellularity of level two walled Brauer algebras, and give a classification of their simple modules over C . This in turn enables us to classify the indecomposable direct summands of the said Tensor modules.
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Highest weight vectors of Mixed Tensor products of general linear Lie superalgebras
arXiv: Quantum Algebra, 2014Co-Authors: Hebing RuiAbstract:In this paper, a notion of cyclotomic (or level $k$) walled Brauer algebras $\mathscr B_{k, r, t}$ is introduced for arbitrary positive integer $k$. It is proven that $\mathscr B_{k, r, t}$ is free over a commutative ring with rank $k^{r+t}(r+t)!$ if and only if it is admissible. Using super Schur-Weyl duality between general linear Lie superalgebras $\mathfrak{gl}_{m|n}$ and $\mathscr B_{2, r, t}$, we give a classification of highest weight vectors of $\mathfrak{gl}_{m|n}$-modules $M_{pq}^{rt}$, the Tensor products of Kac-modules with Mixed Tensor products of the natural module and its dual. This enables us to establish an explicit relationship between $\mathfrak{gl}_{m|n}$-Kac-modules and right cell (or standard) $\mathscr B_{2, r, t}$-modules over $\mathbb C$. Further, we find an explicit relationship between indecomposable tilting $\mathfrak{gl}_{m|n}$-modules appearing in $M_{pq}^{rt}$, and principal indecomposable right $\mathscr B_{2, r, t}$-modules via the notion of Kleshchev bipartitions. As an application, decomposition numbers of $\mathscr B_{2, r, t}$ arising from super Schur-Weyl duality are determined.
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Affine walled Brauer algebras
arXiv: Representation Theory, 2013Co-Authors: Hebing RuiAbstract:A new class of associative algebras referred to as affine walled Brauer algebras are introduced. These algebras are free with infinite rank over a commu- tative ring containing 1. Then level two walled Brauer algebras over C are defined, which are some cyclotomic quotients of affine walled Brauer algebras.We establish a super Schur-Weyl duality between affine walled Brauer algebras and general linear Lie superalgebras, and realize level two walled Brauer algebras as endomorphism al- gebras of Tensor modules of Kac modules with Mixed Tensor products of the natural module and its dual over general linear Lie superalgebras, under some conditions. We also prove the weakly cellularity of level two walled Brauer algebras, and give a classification of their irreducible modules over C. This in turn enables us to classify the indecomposable direct summands of the said Tensor modules.
Wei-qin Zhao - One of the best experts on this subject based on the ideXlab platform.
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Mixed Tensor susceptibility of the QCD vacuum from effective quark-quark interactions
Physics Letters B, 2005Co-Authors: Zhao Zhang, Wei-qin ZhaoAbstract:We calculate the Mixed Tensor susceptibility of QCD vacuum in the framework of the global color symmetry model. In our calculation, the functional integration over gluon fields can be performed and the gluonic vacuum observable can be expressed in terms of the quark operators and the effective gluon correlator. The Mixed Tensor susceptibility was obtained with the subtraction of the perturbative contribution which is evaluated by the Wigner solution of the quark gap equation. Using several different effective quark-quark interaction models, we find the values of the Mixed Tensor susceptibility are very small. (c) 2005 Elsevier B.V. All rights reserved.
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Mixed Tensor susceptibility of the QCD vacuum from effective quark–quark interactions
Physics Letters B, 2005Co-Authors: Zhao Zhang, Wei-qin ZhaoAbstract:AbstractWe calculate the Mixed Tensor susceptibility of QCD vacuum in the framework of the global color symmetry model. In our calculation, the functional integration over gluon fields can be performed and the gluonic vacuum observable can be expressed in terms of the quark operators and the effective gluon correlator. The Mixed Tensor susceptibility was obtained with the subtraction of the perturbative contribution which is evaluated by the Wigner solution of the quark gap equation. Using several different effective quark–quark interaction models, we find the values of the Mixed Tensor susceptibility are very small
Yu I Tipunin - One of the best experts on this subject based on the ideXlab platform.
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bimodule structure of the Mixed Tensor product over uqsl 2 1 and quantum walled brauer algebra
Nuclear Physics, 2018Co-Authors: D.v. Bulgakova, A.m. Kiselev, Yu I TipuninAbstract:Abstract We study a Mixed Tensor product 3 ⊗ m ⊗ 3 ‾ ⊗ n of the three-dimensional fundamental representations of the Hopf algebra U q s l ( 2 | 1 ) , whenever q is not a root of unity. Formulas for the decomposition of Tensor products of any simple and projective U q s l ( 2 | 1 ) -module with the generating modules 3 and 3 ‾ are obtained. The centralizer of U q s l ( 2 | 1 ) on the Mixed Tensor product is calculated. It is shown to be the quotient X m , n of the quantum walled Brauer algebra qw B 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 ⊠ U q s l ( 2 | 1 ) . We give an explicit bimodule structure for all m , n .
I. Yu. Tipunin - One of the best experts on this subject based on the ideXlab platform.
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Bimodule structure of the Mixed Tensor product over Uqsℓ(2|1) and quantum walled Brauer algebra
Nuclear Physics B, 2018Co-Authors: D.v. Bulgakova, A.m. Kiselev, I. Yu. TipuninAbstract:Abstract We study a Mixed Tensor product 3 ⊗ m ⊗ 3 ‾ ⊗ n of the three-dimensional fundamental representations of the Hopf algebra U q s l ( 2 | 1 ) , whenever q is not a root of unity. Formulas for the decomposition of Tensor products of any simple and projective U q s l ( 2 | 1 ) -module with the generating modules 3 and 3 ‾ are obtained. The centralizer of U q s l ( 2 | 1 ) on the Mixed Tensor product is calculated. It is shown to be the quotient X m , n of the quantum walled Brauer algebra qw B 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 ⊠ U q s l ( 2 | 1 ) . We give an explicit bimodule structure for all m , n .