Quantum Cluster Variables via Serre Polynomials

Details Quantum Cluster Variables via Serre Polynomials Quantum Cluster Variables via Serre Polynomials

2010-04-23

arxiv.org/abs/1004.4171v2

Mathematics

Quantum Algebra

minor corrections, reference added, example 4.3 added, 38 pages

Scientific paper

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.

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