On parabolic subgroups of symplectic reflection groups

Abstract Using Cohen’s classification of symplectic reflection groups, we prove that the parabolic subgroups, is, stabilizer a finite group, are themselves groups. This is analog Steinberg’s Theorem for complex computational results required in proof, show nonexistence resolutions quotient singularities corresponding to three exceptional thus reducing further number cases which existence question remains open. Another immediate consequence our result singular locus singularity associated group pure codimension two.