Daniel C. Douglas

activity

20202025

most citedTropical Fock-Goncharov coordinates for

SL_{3}

-webs on surfaces I: construction

6 citations · 10 across the 6 of their papers we have counts for

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6 papers · 1 filter

math.GT2024

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.GT2022

Dimers, webs, and local systems

Daniel C. Douglas, Richard Kenyon, Haolin Shi

For a planar bipartite graph $G$ equipped with a $SL_{n}$ -local system, we show that the determinant of the associated Kasteleyn matrix counts " $n$ -multiwebs" (gene…

math.GT2021★ 3 cited

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…

math.GT2021

Quantum traces for $SL_{n} (C)$ : The case $n = 3$

Daniel C. Douglas

We generalize Bonahon-Wong's $SL_{2} (C)$ -quantum trace map to the setting of $SL_{3} (C)$ . More precisely, given a non-zero complex parameter $q=e^{2…

math.GT2020★ 1 cited

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 $Φ_{T} (W_{3, S^}) \subset Z_{\geq 0}^{N}$ for the collection $…

math.GT2020★ 6 cited

Tropical Fock-Goncharov coordinates for $SL_{3}$ -webs on surfaces I: construction

Daniel C. Douglas, Zhe Sun

For a finite-type surface $S$ , we study a preferred basis for the commutative algebra $C [R_{SL_{3} (C)} (S)]$ of regular func…

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

Dimers, webs, and local systems

Points of quantum SLn​ coming from quantum snakes

Quantum traces for SLn​(C): The case n=3

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

Tropical Fock-Goncharov coordinates for SL3​-webs on surfaces I: construction

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

Quantum traces for $SL_{n} (C)$ : The case $n = 3$

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

Tropical Fock-Goncharov coordinates for $SL_{3}$ -webs on surfaces I: construction