A rational group of hermitian type is a Q-simple algebraic group G such that the symmetric space D of maximal compact subgroups of the real Lie group G(R) is a hermitian symmetric space of the non-compact type. There are two major classes of subgroups of G of importance to the geometry of D and to arithmetic quotients XΓ = Γ\D of D: parabolic subgroups and reductive subgroups. The former are co...

Abstract We show that the geometric realisation of poset proper parabolic subgroups a large-type Artin group has systolic geometry. use this geometry to set is stable under arbitrary intersections and forms lattice for inclusion. As an application, we groups are taking roots completely characterise conjugacy stable. also perspective recover unify results describing normalisers 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 questi...