Abstract
Similar to the symplectic cases, there is a family of 14 orthogonal hypergeometric groups with a maximally unipotent monodromy (cf. Table 1). We show that 2 of the 14 orthogonal hypergeometric groups associated to the pairs of parameters (0, 0, 0, 0, 0), and (0, 0, 0, 0, 0), are arithmetic. We also give a table (cf. Table 2) which lists the quadratic forms Q preserved by these 14 hypergeometric groups, and their two linearly independent Q-orthogonal isotropic vectors in ; it shows in particular that the orthogonal groups of these quadratic forms have -rank two.
Highlights
To explain the results of this paper, we first recall the definition of hypergeometric groups
We show that 2 of the 14 orthogonal hypergeometric groups are arithmetic
), are arithmetic; and the orthogonal hypergeometric group associated to the parameter
Summary
To explain the results of this paper, we first recall the definition of hypergeometric groups. Note that the condition “g(0) = f (0) = 1” ensures that the hypergeometric groups Γ(f, g) are symplectic for all 14 pairs of polynomials f, g. (0, 0, 0, 0, 0)) and g is the product of cyclotomic polynomials such that g(0) = 1, g(1) = 0, and f, g form a primitive pair In this case there are precisely 14 such examples which are determined as follows: if the parameters (0, 0, 0, 0), (β1, β2, β3, β4) correspond to the 14 symplectic hypergeometric groups, the parameters (0, 0, 0, 0, 0),.
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