Bimodule structure of the mixed tensor product over $U_{q} s\ell(2|1)$ and quantum walled Brauer algebra
| Autor: | Bulgakova, D. V., Kiselev, A. M., Tipunin, I. Yu. |
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| Rok vydání: | 2017 |
| Předmět: | |
| Zdroj: | Nucl.Phys. B 928 (2018) 217-257 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.nuclphysb.2018.01.010 |
| Popis: | We study a mixed tensor product $\mathbf{3}^{\otimes m} \otimes \mathbf{\overline{3}}^{\otimes n}$ of the three-dimensional fundamental representations of the Hopf algebra $U_{q} s\ell(2|1)$, whenever $q$ is not a root of unity. Formulas for the decomposition of tensor products of any simple and projective $U_{q} s\ell(2|1)$-module with the generating modules $\mathbf{3}$ and $\mathbf{\overline{3}}$ are obtained. The centralizer of $U_{q} s\ell(2|1)$ on the chain is calculated. It is shown to be the quotient $\mathscr{X}_{m,n}$ of the quantum walled Brauer algebra. The structure of projective modules over $\mathscr{X}_{m,n}$ 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 $\mathscr{X}_{m,n}$. This result forms a crucial step in decomposition of the mixed tensor product as a bimodule over $\mathscr{X}_{m,n}\boxtimes U_{q} s\ell(2|1)$. We give an explicit bimodule structure for all $m,n$. Comment: 43 pages, 5 figures |
| Databáze: | arXiv |
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