ANALYSIS ON INVARIANTS ASSOCIATED WITH PREHOMOGENEOUS VECTOR SPACES FROM THE VIEW POINT OF REPRESENTATION THEORY

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We have studied the b-functions of relative invariants of the prehomogeneous vector spaces associated with quivers of type A. By applying the decomposition formula for b-functions, we determine explicitly the b-functions of one-variable for each irreducible relative invariant. Moreover, we give a graphical algorithm to determine the b-functions of several variables. As its application, we have obtained some results on functional equations of prehomogeneous vector spaces of parabolic type arising from special linear Lie algebras.