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- W2012161907 abstract "We give a complete classification of simple representations of the braid group B_3 with dimension $leq 5$ over any algebraically closed f ield. In particular, we prove that a simple d-dimensional representation $rho: B_3 to GL(V)$ is determined up to isomorphism by the eigenvalues $lambda_1, lambda_2, ..., lambda_d$ of the image of the generators for d=2,3 and a choice of a $delta=sqrt{det rho(sigma_1)}$ for d=4 or a choice of $delta=sqrt[5]{det rho(sigma_1)}$ for d=5. We also s howed that such representations exist whenever the eigenvalues and $delta$ are not roots of certain polynomials $Q_{ij}^{(d)}$, which are explicitly given. In this case, we construct the matrices via which the generators act on V. As an application of our techniques, we also obtain nontrivial q-versions of some of Deligne's formulas for dimensions of representations of exceptional Lie groups." @default.
- W2012161907 created "2016-06-24" @default.
- W2012161907 creator A5026963402 @default.
- W2012161907 creator A5066349307 @default.
- W2012161907 date "1999-12-02" @default.
- W2012161907 modified "2023-09-27" @default.
- W2012161907 title "Representations of the braid group B_3 and of SL(2,Z)" @default.
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