Geodesic
First extension groups of Verma modules and R-polynomials
Noriyuki Abe1
1Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba / Meguro-ku, Tokyo 153--8914, Japan
Journal of Lie Theory, Tome 25 (2015) no. 2, pp. 377-393

Voir la notice de l'article provenant de la source Heldermann Verlag

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

Noriyuki Abe  1

1 Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba / Meguro-ku, Tokyo 153--8914, Japan 
Noriyuki 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/JOLT_2015_25_2_a3/
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     author = {Noriyuki Abe},
     title = {First extension groups of {Verma} modules and {<italic>R</italic>-polynomials}},
     journal = {Journal of Lie Theory},
     pages = {377--393},
     year = {2015},
     volume = {25},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2015_25_2_a3/}
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