For every two sided cell in a Weyl group Lusztig attached a tensor category (via suitably truncated convolution of perverse sheaves on the corresponding flag variety). Moreover, Lusztig proposed a precise conjecture which describes this category in elementary terms. In this talk we report on joint work with R.Bezrukavnikov and M.Finkelberg where this conjecture was proved for almost all two sided cells. On the other hand the conjecture fails in the remaining cases.

Lecture #12674

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