Irreducible factors of modular representations of mapping class groups arising in integral TQFT (Q407399)
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scientific article; zbMATH DE number 6337008
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Irreducible factors of modular representations of mapping class groups arising in integral TQFT |
scientific article; zbMATH DE number 6337008 |
Statements
Irreducible factors of modular representations of mapping class groups arising in integral TQFT (English)
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1 September 2014
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For a surface \(\Sigma\) which is closed or which has one boundary component, the paper under review investigates a modular representation \(F(\Sigma)\) of the mapping class group of \(\Sigma\) induced by an integral version of the Witten--Reshetikhin--Turaev \(SO(3)\) TQFT at the \(p\)th root of unity where \(p\) is an odd prime. They prove that \(F(\Sigma)\) has a composition series with at most \(2\) irreducible factors (Corrolary 2.6) whose dimensions are given by Verline-type formulae (Theorem 2.7). The authors remark that these formulae should also be investigated from a geometric perspective.
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lollipop basis
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topological quantum field theory
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skein theory
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symplectic group
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Verlinde formula
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0.9227678
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0.9118629
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0.9006021
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0.88567543
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0.88447285
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0.8843105
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0.88423175
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