  We study the first extension groups between Verma modules. There was a
conjecture which claims that the dimensions of the higher extension groups
between Verma modules are the coefficients of $R$-polynomials defined by
Kazhdan-Lusztig. This conjecture was known as the Gabber-Joseph conjecture
(although Gebber and Joseph did not state.) However, Boe gives a counterexample
to this conjecture. In this paper, we study how far are the dimensions of
extension groups from the coefficients of $R$-polynomials.
