Computational Tools for Cohomology of Toric Varieties

Table 2

Correlation between zero modes in representations of the GUT group 𝐻.

Number of zero modes in reps. of 𝐻	1	ℎ^1𝑆(𝑉)	ℎ^1𝑆(𝑉^∗)	ℎ^1𝑆(Λ^2𝑉)	ℎ^1𝑆(Λ^2𝑉^∗)	ℎ^1𝑆(𝑉⊗𝑉^∗)
𝐸8				248
↓				↓
𝑆𝑈(3)×𝐸6	(1,78)	⊕ (3,27)	⊕ (3,27)			⊕  (8,1)
𝑆𝑈(4)×𝑆𝑂(10)	(1,45)	⊕ (4,16)	⊕ (4,16)	⊕ (6,10)		⊕ (15,1)
𝑆𝑈(5)×𝑆𝑈(5)	(1,24)	⊕ (5,10)	⊕ (5,10)	⊕ (10,5)	⊕ (10,5)	⊕ (24,1)