The Hall algebra of a cyclic quiver and canonical bases of Fock spaces

  title={The Hall algebra of a cyclic quiver and canonical bases of Fock spaces},
  author={Olivier Schiffmann},
where x ∈ Ŝk is minimal such that ν = λ.x satisfies νi < νi+1 for i = 1, 2 . . . k− 1 and νi− νk ≥ 1− k−n, and μ = λ.x y. This conjecture is proved by Kazhdan-Lusztig [KL] and Kashiwara-Tanisaki [KT]. The proof relies on an equivalence between the category of finite-dimensional Uǫ(slk)-modules and a category of negative-level representations of the affine algebra ŝlk which are integrable with respect to slk. In [VV], Varagnolo and Vasserot propose a new approach to this conjecture, based on the… CONTINUE READING
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