# On Parabolic Subgroups of Symplectic Reflection Groups

@inproceedings{Bellamy2021OnPS, title={On Parabolic Subgroups of Symplectic Reflection Groups}, author={Gwyn Bellamy and Johannes Schmitt and Ulrich Thiel}, year={2021} }

Using Cohen’s classification of symplectic reflection groups, we prove that the parabolic subgroups, that is, stabilizer subgroups, of a finite symplectic reflection group are themselves symplectic reflection groups. This is the symplectic analogue of Steinberg’s Theorem for complex reflection groups. Using computational results required in the proof, we show the non-existence of symplectic resolutions for symplectic quotient singularities corresponding to three exceptional symplectic…

## One Citation

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