A Representation-Theoretic Approach to -Characters - Liu, Henry (Symmetry, Integrability and Geometry: Methods and Applications, 2022)
We raise the question of whether (a slightly generalized notion of) -characters can be constructed purely representation-theoretically. In the main example of the quantum toroidal ₁ algebra, geometric engineering of adjoint matter produces an explicit vertex operator which computes certain -characters, namely Hirzebruch χy-genera, completely analogously to how the -matrix computes -characters. We give a geometric proof of the independence of preferred direction for the refined vertex in this and more general non-toric settings.