Braid group action on projective quantum \(\mathfrak{sl}(2)\) modules (Q2043346)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Braid group action on projective quantum \(\mathfrak{sl}(2)\) modules |
scientific article |
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Braid group action on projective quantum \(\mathfrak{sl}(2)\) modules (English)
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30 July 2021
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In this paper, the author studies the action of the braid group \(B_n\) on \(V_{r-1}^{\otimes n}\), where \(V_{r-1}\) is the Steinberg module of dimension \(r\). In particular, using the Jackson-Kerler method to the root of unity case, the author obtains a family of representations \(B_n \rightarrow \mathrm{GL}(\mathbb C)\), and extends these representations non-trivially.
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braid group representations
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quantum groups
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projective modules
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Lawrence representations
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