Daniel C. Douglas

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math.GT2026

Monomial web basis for the SL(N) skein algebra of the twice punctured sphere

Tommaso Cremaschi, Daniel C. Douglas

We give a new proof of a slightly modified version of a result of Queffelec--Rose, by constructing a linear basis for the $SL (n)$ skein algebra of the twice punctured sphe…

math.GT2025

Tropical Fock-Goncharov coordinates for $SL_{3}$ -webs on surfaces II: naturality

Daniel C. Douglas, Zhe Sun

In a companion paper (arXiv 2011.01768), we constructed nonnegative integer coordinates $I^¦_{T} (W_{3, S^}) \subset Z_{\geq 0}^{N}$ for the collection…

math.GT2025

Points of quantum $SL_{n}$ coming from quantum snakes

Daniel C. Douglas

We show that the quantized Fock-Goncharov monodromy matrices satisfy the relations of the quantum special linear group $SL_{n}^{q}$ . The proof employs a quantum version of the…

Monomial web basis for the SL(N) skein algebra of the twice punctured sphere

Tropical Fock-Goncharov coordinates for SL3​-webs on surfaces II: naturality

Points of quantum SLn​ coming from quantum snakes

Tropical Fock-Goncharov coordinates for $SL_{3}$ -webs on surfaces II: naturality

Points of quantum $SL_{n}$ coming from quantum snakes