Singular invariant hyperfunctions on the space of real symmetric matrices of size n are discussed in this paper. We construct singular invariant hyperfunctions, i.e., invariant hyperfunctions whose supports are contained in the set of the points of rank strictly less than n, in terms of negative order coefficients of the Laurent expansions of the complex powers of the determinant function. In particular, we give an algorithm to determine the orders of poles of the complex powers of the determinant functions and the support of the singular hyperfunctions appearing in the principal part of the Laurent expansions of the complex powers.
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