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| Format: | Preprint |
| Published: |
2010
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1003.0169 |
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Table of Contents:
- 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.