• Corpus ID: 209515931

On singularity properties of word maps and applications to probabilistic Waring type problems

@article{Glazer2019OnSP,
  title={On singularity properties of word maps and applications to probabilistic Waring type problems},
  author={Itay Glazer and Yotam I. Hendel},
  journal={arXiv: Algebraic Geometry},
  year={2019}
}
We study singularity properties of word maps on semisimple algebraic groups and Lie algebras, generalizing the work of Aizenbud-Avni in the case of the commutator map. Given a word $w$ in a free Lie algebra $\mathcal{L}_{r}$, it induces a word map $\varphi_{w}:\mathfrak{g}^{r}\rightarrow\mathfrak{g}$ for every semisimple Lie algebra $\mathfrak{g}$. Given two words $w_{1}\in\mathcal{L}_{r_{1}}$ and $w_{2}\in\mathcal{L}_{r_{2}}$, we define and study the convolution of the corresponding word maps… 
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