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arXiv · 1807.07539

An expansion formula for type A and Kronecker quantum cluster algebras

Ilke Canakci·Philipp Lampe
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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.

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Ilke Canakci, Philipp Lampe. 2018-07-19. An expansion formula for type A and Kronecker quantum cluster algebras. https://arxiv.org/abs/1807.07539

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