• A
  • A
  • A
  • ABC
  • ABC
  • ABC
  • А
  • А
  • А
  • А
  • А
Regular version of the site

Working paper

Generalized Slices for Minuscule Cocharacters

Krylov V., Перунов И.
Let G be a connected reductive complex algebraic group with a maximal torus T. We denote by Λ the cocharacter lattice of (T,G). Let Λ^+⊂Λ be the submonoid of dominant coweights. For λ∈Λ+,μ∈Λ,μ⩽λ, in arXiv:1604.03625, authors defined a generalized transversal slice W^λ_μ. This is an algebraic variety of the dimension ⟨2ρ^∨,λ−μ⟩, where 2ρ^∨ is the sum of positive roots of G. We prove that for a minuscule λ and μ appearing as a weight of V^λ (irreducible representation of the Langlands dual group G^∨ with the highest weight λ) the variety W^λ_μ is isomorphic to the affine space 𝔸⟨2ρ^∨,λ−μ⟩ and that in certain coordinates the Poisson structure on it is standard.