Geodesic
On parabolic subgroups of symplectic reflection groups
Glasgow mathematical journal, Tome 65 (2023) no. 2, pp. 401-413

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DOI

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 analog of Steinberg’s Theorem for complex reflection groups.Using computational results required in the proof, we show the nonexistence of symplectic resolutions for symplectic quotient singularities corresponding to three exceptional symplectic reflection groups, thus reducing further the number of cases for which the existence question remains open.Another immediate consequence of our result is that the singular locus of the symplectic quotient singularity associated to a symplectic reflection group is pure of codimension two.
DOI : 10.1017/S0017089522000416
Mots-clés : Symplectic reflection groups, parabolic subgroups, symplectic resolutions, Steinberg’s fixed point theorem 
Bellamy, Gwyn; Schmitt, Johannes; Thiel, Ulrich. On parabolic subgroups of symplectic reflection groups. Glasgow mathematical journal, Tome 65 (2023) no. 2, pp. 401-413. doi: 10.1017/S0017089522000416
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     year = {2023},
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