Quantum Cluster Variables via Serre Polynomials

Understand

For skew-symmetric acyclic quantum cluster algebras, we express the quantum $F$-polynomials and the quantum cluster monomials in terms of Serre polynomials of quiver Grassmannians of rigid modules.

• As byproducts, we obtain the existence of counting polynomials for these varieties and the positivity conjecture with respect to acyclic seeds.
• These results complete previous work by Caldero and Reineke and confirm a recent conjecture by Rupel.