Infinite family of equi-isoclinic planes in Euclidean odd dimensional spaces and of complex symmetric conference matrices of odd orders
Abstract
A n-set of equi-isoclinic planes in Rr is a set of n planes spanning Rr each pair of which has the same non-zero angle arccos(sqrt(lambda)). We prove that for any odd integer k such that 2k=palpha+1, p odd prime, alpha non-negative integer the maximum number of equi-isoclinic planes with angle arccos(sqrt(1/(2k-2))) in R(2k-1) is equal to 2k-1. The solution of this geometric problem is obtained by the construction of complex conference matrices of order 2k-1.
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