Orthogonal Hypergeometric Groups with a Maximally Unipotent Monodromy

Abstract

Similar to the symplectic cases, there is a family of fourteen orthogonal hypergeometric groups with a maximally unipotent monodromy (cf. Table 1.1). We show that two of the fourteen orthogonal hypergeometric groups associated to the pairs of parameters $(0,0,0,0,0)$, $(\frac{1}{6},\frac{1}{6},\frac{5}{6},\frac{5}{6},\frac{1}{2})$; and $(0,0,0,0,0)$, $(\frac{1}{4},\frac{1}{4},\frac{3}{4},\frac{3}{4},\frac{1}{2})$ are arithmetic. We also give a table (cf. Table 2.1) which lists the quadratic forms $\mathrm{Q}$ preserved by these fourteen hypergeometric groups, and their two linearly independent $\mathrm{Q}$- orthogonal isotropic vectors in ${\mathbb{Q}}^5$; it shows in particular that the orthogonal groups of these quadratic forms have $\mathbb{Q}$- rank two.

Final version; accepted for publication in Experimental Mathematics

References in corpus (1)

• Mirror Symmetry and Integral Variations of Hodge Structure Underlying One Parameter Families of Calabi-Yau Threefolds