Buildings, spiders, and geometric Satake
Quantum Algebra
2019-09-16 v2 Geometric Topology
Representation Theory
Abstract
Let G be a simple algebraic group. Labelled trivalent graphs called webs can be used to product invariants in tensor products of minuscule representations. For each web, we construct a configuration space of points in the affine Grassmannian. Via the geometric Satake correspondence, we relate these configuration spaces to the invariant vectors coming from webs. In the case G = SL(3), non-elliptic webs yield a basis for the invariant spaces. The non-elliptic condition, which is equivalent to the condition that the dual diskoid of the web is CAT(0), is explained by the fact that affine buildings are CAT(0).
Cite
@article{arxiv.1103.3519,
title = {Buildings, spiders, and geometric Satake},
author = {Bruce Fontaine and Joel Kamnitzer and Greg Kuperberg},
journal= {arXiv preprint arXiv:1103.3519},
year = {2019}
}
Comments
49 pages; revised and to appear in Compositio Mathematica