The representation theory of the Temperley-Lieb algebras¶
Westbury, B. W. (1995). The representation theory of the Temperley-Lieb algebras. Mathematische Zeitschrift.
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Domain-specific¶
- Temperley–Lieb Algebra
- Generic parameters over a suitable characteristic-zero field give semisimplicity, while special values—especially root-of-unity specializations in common \(q\)-conventions—produce radicals, reducible standard modules, and important quotients
This sourceWestbury computes the determinant of the invariant bilinear form on the standard modules, giving the criterion that separates the generic (semisimple) parameters from the root-of-unity specialisations where radicals appear; later work corrects an error in his recursion.
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- Generic parameters over a suitable characteristic-zero field give semisimplicity, while special values—especially root-of-unity specializations in common \(q\)-conventions—produce radicals, reducible standard modules, and important quotients
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