English

Equivariant degenerations of spherical modules for groups of type A

Algebraic Geometry 2015-09-18 v3 Representation Theory

Abstract

Let G be a complex reductive algebraic group. Fix a Borel subgroup B of G, with unipotent radical U, and a maximal torus T in B with character group X(T). Let S be a submonoid of X(T) generated by finitely many dominant weights. V. Alexeev and M. Brion introduced a moduli scheme M_S which classifies pairs (X,f) where X is an affine G-variety and f is a T-equivariant isomorphism between the categorical quotient of X by U and the toric variety determined by S. In this paper, we prove that M_S is isomorphic to an affine space when S is the weight monoid of a spherical G-module with G of type A.

Keywords

Cite

@article{arxiv.1008.0911,
  title  = {Equivariant degenerations of spherical modules for groups of type A},
  author = {Stavros Argyrios Papadakis and Bart Van Steirteghem},
  journal= {arXiv preprint arXiv:1008.0911},
  year   = {2015}
}

Comments

v3: 65 pages, minor corrections and changes to exposition following referee's suggestions, a shorter version will appear in Annales de l'Institut Fourier