First extension groups of Verma modules and $R$-polynomials
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2010
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| _version_ | 1866913653771468800 |
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| author | Abe, Noriyuki |
| author_facet | Abe, Noriyuki |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1003_0169 |
| institution | arXiv |
| publishDate | 2010 |
| record_format | arxiv |
| spellingShingle | First extension groups of Verma modules and $R$-polynomials Abe, Noriyuki Representation Theory 17B10, 17B55 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. |
| title | First extension groups of Verma modules and $R$-polynomials |
| topic | Representation Theory 17B10, 17B55 |
| url | https://arxiv.org/abs/1003.0169 |