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Mathematics > Quantum Algebra

arXiv:1807.07539 (math)
[Submitted on 19 Jul 2018 (v1), last revised 19 Sep 2018 (this version, v2)]

Title:An expansion formula for type A and Kronecker quantum cluster algebras

Authors: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.
Comments: 22 pages
Subjects: Quantum Algebra (math.QA); Combinatorics (math.CO); Rings and Algebras (math.RA)
MSC classes: 13F60, 17B37, 05C30
Cite as: arXiv:1807.07539 [math.QA]
  (or arXiv:1807.07539v2 [math.QA] for this version)
  https://doi.org/10.48550/arXiv.1807.07539

Submission history

From: Ilke Canakci [view email]
[v1] Thu, 19 Jul 2018 17:10:01 UTC (31 KB)
[v2] Wed, 19 Sep 2018 09:52:15 UTC (64 KB)
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