Abstract
We study the diagrammatic Hecke category associated with the affine Weyl group of type \(\tilde{A}_2 \). More precisely we find a (surprisingly simple) basis in characteristic zero for the Hom spaces between indecomposable objects, that we call indecomposable double leaves.
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Notes
For \(n\le 3\) the elements \(y_n\) and \(z_n\) are not well-defined. However, for those n, the corresponding coefficients \(c_{n+1}\) and \(d_{n+1}\) in the projectors vanish.
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Acknowledgements
We thank Geordie Williamson for sharing with us theorem 1 (without a proof) and for suggesting Problem A for \(SL_3\). We thank the referee for the very thorough correction. The first author acknowledges the financial support of Fondecyt Proyecto Regular 1200061.
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