Smoothness of Quotients Associated With a Pair of Commuting Involutions
Copyright policy )Smoothness of Quotients Associated With a Pair of Commuting Involutions
AbstractLet σ, θ be commuting involutions of the connected semisimple algebraic group G where σ, θ and G are defined over an algebraically closed field , char = 0. Let H := Gσ and K := Gθ be the fixed point groups. We have an action (H × K) × G → G, where ((h, k), g) ⟼ hgk–1, h ∈ H, k ∈ K, g ∈ G. Let G//(H × K) denote the categorical quotient Spec (G)H×K. We determine when this quotient is smooth. Our results are a generalization of those of Steinberg [Ste75], Pittie [Pit72] and Richardson [Ric82] in the symmetric case where σ = θ and H = K.
- North Carolina Agricultural and Technical State University United States
- Brandeis University United States
Semisimple Lie groups and their representations, connected reductive algebraic groups, Group actions on varieties or schemes (quotients), Linear algebraic groups over the reals, the complexes, the quaternions, categorical quotients, Grassmannians, Schubert varieties, flag manifolds, Linear algebraic groups over arbitrary fields, commuting involutions
Semisimple Lie groups and their representations, connected reductive algebraic groups, Group actions on varieties or schemes (quotients), Linear algebraic groups over the reals, the complexes, the quaternions, categorical quotients, Grassmannians, Schubert varieties, flag manifolds, Linear algebraic groups over arbitrary fields, commuting involutions
citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).4 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!