Olivier Schiffmann
Université Paris-Sud, Orsay, France

Let $X$ be a smooth projective curve of genus $g$ defined over a finite field $\mathbb{F}_q$. For $n \geq 1$ and $d \in \mathbb{Z}$, let $$C^{cusp}_{n,d} \subset Fun(Bun_{n,d}(X),\mathbb{C})$$ denote the space of (everywhere unramified) cuspidal function of rank $n$ and degree $d$. Its dimension was explicitly computed a few years ago by Hongjie Yu, in terms of the so-called Kac polynomials of curves. Using the theory of cohomological Hall algebras, we propose a Lie-theoretic interpretation of this space (at least, of its dimension), and associate to it a module (of that dimension) over an algebra slightly larger than the usual Hecke algebra.