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  1. Clingher, Adrian (Ed.)
    Abstract Green–Griffiths–Kerr introduced Hodge representations to classify the Hodge groups of polarized Hodge structures, and the corresponding Mumford–Tate subdomains. We summarize how, given a fixed period domain $$ \mathcal{D} $$ , to enumerate the Hodge representations and corresponding Mumford–Tate subdomains $$ D \subset \mathcal{D} $$ . The procedure is illustrated in two examples: (i) weight two Hodge structures with $$ {p}_g={h}^{2,0}=2 $$ ; and (ii) weight three CY-type Hodge structures. 
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