Generating basis webs for $\SL_n$

Details Generating basis webs for $\SL_n$ Generating basis webs for $\SL_n$

2011-08-23

arxiv.org/abs/1108.4616v1

Mathematics

Quantum Algebra

Scientific paper

Given a simple algebraic group $G$, a web is a directed trivalent graph with edges labelled by dominant minuscule weights. There is a natural surjection of webs onto the invariant space of tensor products of minuscule representations. Following the work of Westbury, we produce a set of webs for $\SL_n$ which form a basis for the invariant space via the geometric Satake correspondence. In fact, there is an upper unitriangular change of basis to the Satake basis. This set of webs agrees with previous work in the cases $n=2,3$ and generalizes the work of Westbury in the case $n\geq 4$.

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