The minimal degeneration singularities in the affine Grassmannians

TL;DR

This paper classifies the minimal degeneration singularities in affine Grassmannians of simple algebraic groups, identifying them as Kleinian singularities or nilpotent orbit closures, and extends the analysis to non-simply-laced types using advanced cohomological methods.

Contribution

It provides a complete classification of minimal degeneration singularities in affine Grassmannians for all types, including non-simply-laced groups, using intersection cohomology and Chow groups.

Findings

Minimal degeneration singularities are Kleinian type A or nilpotent orbit closures.

Singularities for non-simply-laced types are characterized via intersection cohomology.

The classification extends to all simple algebraic groups.

Abstract

The minimal degeneration singularities in the affine Grassmannians of simple simply-laced algebraic groups are determined to be either Kleinian singularities of type A, or closures of minimal orbits in nilpotent cones. The singularities for non-simply-laced types are studied by intersection cohomology and equivariant Chow group methods.