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Buildings, spiders, and geometric Satake

  • Bruce Fontaine (a1), Joel Kamnitzer (a2) and Greg Kuperberg (a3)

Abstract

Let $G$ be a simple algebraic group. Labelled trivalent graphs called webs can be used to produce 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 of $G= \mathrm{SL} (3)$ , 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 $\mathrm{CAT} (0)$ , is explained by the fact that affine buildings are $\mathrm{CAT} (0)$ .

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References

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Buildings, spiders, and geometric Satake

  • Bruce Fontaine (a1), Joel Kamnitzer (a2) and Greg Kuperberg (a3)

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