2000 character limit reached
An expansion formula for type A and Kronecker quantum cluster algebras (1807.07539v2)
Published 19 Jul 2018 in math.QA, math.CO, and math.RA
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.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Collections
Sign up for free to add this paper to one or more collections.
