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4
votes
Accepted
Do the following two filtrations of the affine Grassmannian agree?
This statement isn't true; as you've currently defined everything, your $X_i$ are infinite dimensional (in fact they are unions of connected components.) You want instead to take the $X_i$ unions of $ …
7
votes
Why should affine lie algebras and quantum groups have equivalent representation theories?
(Written on my phone - apologies for any typos.)
A few comments:
a) First, as to the source of the braided monoidal structure on the Kazhdan-Lusztig category. The category of integrable affine Lie …