Buildings, spiders, and geometric Satake

Details Buildings, spiders, and geometric Satake Buildings, spiders, and geometric Satake

2011-03-17

arxiv.org/abs/1103.3519v1

Mathematics

Quantum Algebra

46 pages

Scientific paper

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).

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