An expansion formula for type A and Kronecker quantum cluster algebras
Quantum Algebra
2018-09-20 v2 Combinatorics
Rings and Algebras
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 case, 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.
Keywords
Cite
@article{arxiv.1807.07539,
title = {An expansion formula for type A and Kronecker quantum cluster algebras},
author = {Ilke Canakci and Philipp Lampe},
journal= {arXiv preprint arXiv:1807.07539},
year = {2018}
}
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22 pages