arXiv:1003.0169 [math.RT]AbstractReferencesReviewsResources
First extension groups of Verma modules and $R$-polynomials
Published 2010-02-28, updated 2025-01-17Version 2
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.
Comments: 16 pages, one of the main theorems was false, erratum is added
Categories: math.RT
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