Journal of Lie Theory

no. 2
First extension groups of Verma modules and R-polynomials
Journal of Lie Theory, Volume 25 (2015) no. 2, pp. 377-393
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 it.) However, Boe gives a counterexample to this conjecture. In this paper, we study how far the dimensions of extension groups from the coefficients of R-polynomials are.
DOI: 10.5802/jolt.841
Classification: 17B10, 17B55
Keywords: Verma module, Extension groups 
@article{JOLT_2015_25_2_a3,
     author = {N. Abe},
     title = {First extension groups of {Verma} modules and {R-polynomials}},
     journal = {Journal of Lie Theory},
     pages = {377--393},
     year = {2015},
     volume = {25},
     number = {2},
     doi = {10.5802/jolt.841},
     zbl = {1394.17014},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.841/}
}
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N. Abe. First extension groups of Verma modules and R-polynomials. Journal of Lie Theory, Volume 25 (2015) no. 2, pp. 377-393. doi: 10.5802/jolt.841

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