On matrices arising in the finite field analogue of Euler's integral transform (Q401760)

Summary: \textit{J. Greene} [Character sum analogues for hypergeometric and generalized hypergeometric functions over finite fields. Ph. D. thesis, Ann Arbor (1984), p. 133] defined an analogue of the Euler integral transform for finite field hypergeometric series. Here we consider a special family of matrices which arise naturally in the study of this transform and prove a conjecture of Ono about the decomposition of certain finite field hypergeometric functions into functions of lower dimension.