Microlocal approach to Lusztig's symmetries
  We reformulate the De Concini -- Toledano Laredo conjecture about the monodromy of the Casimir connection in terms of a relation between Lusztig's symmetries of quantum group modules and the monodromy in the vanishing cycles of factorizable sheaves. 
Michael Finkelberg and Vadim Schechtman
math.AG math.QA math.RT