Buildings, spiders, and geometric Satake
2013 ◽
Vol 149
(11)
◽
pp. 1871-1912
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Keyword(s):
AbstractLet$G$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$\mathrm{CAT} (0)$.
1971 ◽
Vol 12
(1)
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pp. 1-14
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2020 ◽
pp. 027836492093299
Keyword(s):
1976 ◽
Vol 79
(2)
◽
pp. 136-151
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Keyword(s):
2002 ◽
Vol 05
(02)
◽
pp. 201-233
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1996 ◽
Vol 11
(05)
◽
pp. 823-843