Geodesic
First extension groups of Verma modules and R-polynomials
Journal of Lie theory, Tome 25 (2015) no. 2, pp. 377-393
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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.
Classification : 17B10, 17B55
Mots-clés : Verma module, Extension groups 
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     author = {N. Abe},
     title = {First extension groups of {Verma} modules and {\protect\emph{R}-polynomials}},
     journal = {Journal of Lie theory},
     pages = {377--393},
     year = {2015},
     volume = {25},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JLT_2015_25_2_JLT_2015_25_2_a3/}
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N. Abe. First extension groups of Verma modules and R-polynomials. Journal of Lie theory, Tome 25 (2015) no. 2, pp. 377-393. http://geodesic.mathdoc.fr/item/JLT_2015_25_2_JLT_2015_25_2_a3/