{"ID":23543106,"CreatedAt":"2026-09-18T03:57:46.008101424Z","UpdatedAt":"2026-09-18T03:57:46.008101424Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.20049","arxiv_id":"2609.20049","title":"A refined multiplication formula in 2-Calabi-Yau Frobenius extriangulated categories","abstract":"We prove a multiplication formula for the Wang-Wei-Zhang cluster character on a Hom-finite $2$-Calabi--Yau Frobenius extriangulated category $\\mathcal C$ with a cluster-tilting object under the assumption that its stable category has constructible cones with respect to the induced cluster-tilting object. This formula generalizes those obtained by Wang-Wei-Zhang for $\\mathcal C$ in the one-dimensional case and by Keller-Plamondon-Qin for (stably) $2$-Calabi-Yau Frobenius or triangulated categories. As a consequence, we express the frozen term in an Auslander-Reiten mesh with the character of a minimal cosyzygy middle term. For acyclic quivers with principal coefficients, we compute these frozen multiplicities in Higgs categories and obtain explicit principal coefficient mesh relations.","short_abstract":"We prove a multiplication formula for the Wang-Wei-Zhang cluster character on a Hom-finite $2$-Calabi--Yau Frobenius extriangulated category $\\mathcal C$ with a cluster-tilting object under the assumption that its stable category has constructible cones with respect to the induced cluster-tilting object. This formula g...","url_abs":"https://arxiv.org/abs/2609.20049","url_pdf":"https://arxiv.org/pdf/2609.20049v1","authors":"[\"Ming Ding\",\"Fan Xu\",\"Panyue Zhou\"]","published":"2026-09-17T10:54:10Z","proceeding":"math.RT","tasks":"[\"math.RT\",\"math.CT\"]","methods":"[]","has_code":false}