Equivalent combinatorial expansion formulas for generalized cluster algebras on punctured orbifolds are derived using snake graphs, labelled posets, matrices, and T-walks, generalizing prior results for surfaces and unpunctured orbifolds.
arXiv preprint arXiv:2301.11101 , year=
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Introduces birational Weyl group action on symplectic groupoid of A_n matrices via cluster transformations and proves invariants form finite central extension of matrix entry algebra, with applications to Teichmuller images and DT-transformations.
For polygonal surfaces, the localized stated SL_n-skein algebra equals the associated quantum cluster algebra, producing a rotation-invariant basis.
SL(n) skein algebra of the twice punctured sphere is a commutative polynomial algebra in n-1 explicit crossing-free web generators for generic q.
Constructs quantized trace-of-monodromy via Bonahon-Wong maps and verifies Teschner recursion plus strong commutation for disjoint loops in Chekhov-Fock quantum Teichmüller theory.
citing papers explorer
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Cluster Expansions from Punctured Orbifolds
Equivalent combinatorial expansion formulas for generalized cluster algebras on punctured orbifolds are derived using snake graphs, labelled posets, matrices, and T-walks, generalizing prior results for surfaces and unpunctured orbifolds.
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Birational Weyl Group Action on the Symplectic Groupoid and Cluster Algebras
Introduces birational Weyl group action on symplectic groupoid of A_n matrices via cluster transformations and proves invariants form finite central extension of matrix entry algebra, with applications to Teichmuller images and DT-transformations.
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Quantum cluster algebra realization for stated ${\rm SL}_n$-skein algebras and rotation-invariant bases for polygons
For polygonal surfaces, the localized stated SL_n-skein algebra equals the associated quantum cluster algebra, producing a rotation-invariant basis.
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Monomial web basis for the SL(N) skein algebra of the twice punctured sphere
SL(n) skein algebra of the twice punctured sphere is a commutative polynomial algebra in n-1 explicit crossing-free web generators for generic q.
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Quantized Geodesic Lengths for Teichm\"uller Spaces: Algebraic Aspects
Constructs quantized trace-of-monodromy via Bonahon-Wong maps and verifies Teschner recursion plus strong commutation for disjoint loops in Chekhov-Fock quantum Teichmüller theory.