Highest weight modules and \(b\)-functions of semi-invariants (Q1343235)

The author gave a criterion for irreducibility of generalized Verma modules in a preceding paper, where the author clarified that the irreducibility is closely connected with the roots of \(b\)-functions of semi-invariants. Thus, in order to judge when the generalized Verma module is irreducible, it is necessary to calculate the \(b\)-functions of semi-invariants. In this paper, the author develops techniques to compute \(b\)-functions and formulates a new conjecture which would eliminate a restriction of the criterion given in the preceding paper. This paper contains many interesting examples of the calculations of holonomy diagrams. They would give us remarkable information on micro-local structure of semi-invariants.