Representations of Deligne-Mostow lattices into

Figures & data

Table 1 Compact three-fold Deligne-Mostow Lattices.

(p, k)	Total	Galois Orbits	$\mathbb{Q}-$extension	Irreducible	Reducible
(3,4)	18	2	$\mathbf{\mathbb{Q}}({\mathbf{\zeta }}_{\mathbf{36}})$	1	0
			$\mathbb{Q}({\zeta }_{18})$	1	0
(3,5)	24	1	$\mathbf{\mathbb{Q}}({\mathbf{\zeta }}_{\mathbf{45}})$	1	0
(4,3)	20	5	$\mathbf{\mathbb{Q}}({\mathbf{\zeta }}_{\mathbf{36}})$	3	0
			$\mathbb{Q}$	0	(0,2)
(5,2)	12	2	$\mathbf{\mathbb{Q}}({\mathbf{\zeta }}_{\mathbf{15}})$	1	0
			$\mathbb{Q}({\zeta }_{10})$	1	0
(5,3)	25	2	$\mathbf{\mathbb{Q}}({\mathbf{\zeta }}_{\mathbf{45}})$	1	0
			$\mathbb{Q}$	0	(0,1)

Table 2 Non-compact three3-fold Deligne-Mostow Lattices.

(p, k)	Total	Galois Orbits	$\mathbb{Q}-$extension	Irreducible	Reducible	Hermitian Form	Factors
(3,6)	39	14	$\mathbf{\mathbb{Q}}({\mathbf{\zeta }}_{\mathbf{9}})$	1	0	(2,1)	0
				2	0	(3,0)	2
			$\mathbb{Q}({\zeta }_3)$	0	(6,4)	Degenerate	10
			$\mathbb{Q}$	0	(0,1)	Degenerate	1
(4,4)	26	13	$\mathbb{Q}({\zeta }_{12})$	1	0	(2,1)	0
				1	0	(3,0)	1
				0	(2,2)	Degenerate	4
			$\mathbb{Q}({\zeta }_6)$	2	0	(3,0)	2
			$\mathbf{\mathbb{Q}}({\mathbf{\zeta }}_{\mathbf{4}})$	1	0	(2,1)	0
				0	(2,0)	Degenerate	2
			$\mathbb{Q}$	1	(0,1)	Degenerate	2
(6,2)	13	5	$\mathbf{\mathbb{Q}}({\mathbf{\zeta }}_{\mathbf{18}})$	1	0	(2,1)	0
				1	0	(3,0)	1
			$\mathbb{Q}({\zeta }_6)$	1	0	(3,0)	1
			$\mathbb{Q}$	1	0	(3,0)	1
				0	(0,1)	Degenerate	1
(6,3)	44	19	$\mathbf{\mathbb{Q}}({\mathbf{\zeta }}_{\mathbf{9}})$	1	0	(2,1)	0
				2	0	(3,0)	2
			$\mathbb{Q}({\zeta }_3)$	0	(6,8)	Degenerate	12
			$\mathbb{Q}$	0	(0,2)	Degenerate	2