First extension groups of Verma modules and R-polynomials

2010/02/28 by Noriyuki Abe, Abe, Noriyuki · 1 citation
Mathematics · #17B10 #17B55 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1003.0169

openalex publication_date 2010/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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