%0 Journal Article
%T First extension groups of Verma modules and $R$-polynomials
%A Noriyuki Abe
%J Mathematics
%D 2010
%I arXiv
%X 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.
%U http://arxiv.org/abs/1003.0169v1