Vertex operators and character varieties
  We prove some combinatorial conjectures extending those proposed in [13, 14]. The proof uses a vertex operator due to Nekrasov, Okounkov, and the first author [4] to obtain a "gluing formula" for the relevant generating series, essentially reducing the computation to the case of complex projective space with three punctures. 
Erik Carlsson and Fernando Rodriguez-Villegas
math.AG math.RT