## Abstract

In the present paper, we consider word maps w: G^{m} → G and word maps with constants w_{Σ}: G^{m} → G of a simple algebraic group G, where w is a nontrivial word in the free group F_{m} of rank m, w_{Σ} = w_{1}σ_{1}w_{2} ··· w_{r}σ_{r}w_{r + 1}, w_{1}, …, w_{r + 1} ∈ F_{m}, w_{2}, …, w_{r} ≠ 1, Σ = {σ_{1}, …, σ_{r} | σ_{i} ∈ GZ(G)}. We present results on the images of such maps, in particular, we prove a theorem on the dominance of “general” word maps with constants, which can be viewed as an analogue of a well-known theorem of Borel on the dominance of genuine word maps. Besides, we establish a relationship between the existence of unipotents in the image of a word map and the structure of the representation variety R(Γ_{w}, G) of the group Γ_{w} = F_{m}/<w>.

Original language | English |
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Pages (from-to) | 632-634 |

Number of pages | 3 |

Journal | Doklady Mathematics |

Volume | 94 |

Issue number | 3 |

DOIs | |

State | Published - 1 Nov 2016 |

### Bibliographical note

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