Orthogonal Hypergeometric Groups with a Maximally Unipotent Monodromy

2014/06/23 by Sandip Singh, Singh, Sandip
Computer Science · Mathematics · #Advanced Algebra and Geometry #Coding theory and cryptography #Finite Group Theory Research #math.GR #msc:22E40

paper · pdf · doi:10.48550/arxiv.1406.5861

Final version; accepted for publication in Experimental Mathematics

arxiv created 2015/03/10 · arxiv updated 2015/03/11

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), ((1)/(6), (1)/(6), (5)/(6), (5)/(6), (1)/(2)); and (0, 0, 0, 0, 0), ((1)/(4), (1)/(4), (3)/(4), (3)/(4), (1)/(2)) are arithmetic. We also give a table (cf. Table 2.1) which lists the quadratic forms Q preserved by these fourteen hypergeometric groups, and their two linearly independent Q- orthogonal isotropic vectors in ℚ⁵; it shows in particular that the orthogonal groups of these quadratic forms have ℚ- rank two.

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