Examines extension groups in Verma modules, revealing discrepancies with R-polynomial coefficients, suggesting deeper mathematical implications.
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 Gabber 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.
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N. Abe (2015) studied this question.
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