Geodesic
On the image of a word map with constants of a simple algebraic group II
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 35, Tome 492 (2020), pp. 75-93 Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper is a continuation of the investigations of images of word maps with constants $\widetilde{w}_\Sigma: G^n \rightarrow G$ on a simple algebraic group $G$ started in the work of F. Gnutov and N. Gordeev, On the image of a word map with constants of a simple algebraic group, Zap. Nauchn. Semin. POMI, 478 (2019), 78–99. In this paper we prove that for adjoint simple algebraic groups of the type $B_l, C_l, F_4, G_2$ over a field of characteristic $\ne 2, 3$ the map $\pi\circ \widetilde{w}$, where $\widetilde{w}_\Sigma$ is word map without small constants and $\pi: G\rightarrow T/W$ is a map of factorization, is a constant map if and only if $w_\Sigma=vgv^{-1}$, where $g \in G$ and $v$ is a word with constants. Also, we give estimates for dimensions of images of some types of word maps with constants on simple algebraic groups. 
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F. A. Gnutov. On the image of a word map with constants of a simple algebraic group II. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 35, Tome 492 (2020), pp. 75-93. http://geodesic.mathdoc.fr/item/ZNSL_2020_492_a6/

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