Abstract
We introduce an expansion formula for elements in quantum cluster algebras associated to type A and Kronecker quivers with principal quantization. Our formula is parametrized by perfect matchings of snake graphs as in the classical case. In the Kronecker type, the coefficients are q-powers whose exponents are given by a weight function induced by the lattice of perfect matchings. As an application, we prove that a reflectional symmetry on the set of perfect matchings satisfies Stembridge's q=−1 phenomenon with respect to the weight function. Furthermore, we discuss a relation of our expansion formula to generating functions of BPS states.
Original language | English |
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Article number | 105132 |
Pages (from-to) | 1-30 |
Number of pages | 30 |
Journal | Journal of Combinatorial Theory. Series A |
Volume | 171 |
Early online date | 31 Oct 2019 |
DOIs | |
Publication status | Published - Apr 2020 |
Keywords
- Arcs
- Lattices
- Mathematical physics
- Non-commutative rings
- Perfect matchings
- Quantum cluster algebras
- Snake graphs
- Stembridge phenomenon
- Surface cluster algebras
- Triangulations