# 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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