2005/02/09 by Brian Parshall, B. Parshall, Parshall, B. +3
Mathematics · #17B55 #20G #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:17B55 #msc:20G
paper · pdf · doi:10.48550/arxiv.math/0502191
arxiv created 2005/02/09 · openalex publication_date 2005/02/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper consists of three interconnected parts. Parts I,III study the relationship between the cohomology of a reductive group and that of a Levi subgroup. For example, we provide a necessary condition, arising from Kazhdan-Lusztig theory, for the natural map on Ext-groups of irreducible modules to be surjective. In cohomological degree 1, the map is always an isomorphism, under our hypothesis. These results were inspired by recent work of Hemmer obtained for general linear groups, and they both extend and improve upon his work when our condition is met. Part II obtains results on Lusztig character formulas for reductive groups, obtaining new necessary and sufficient conditions for such formulas to hold. In the special case of general linear groups, these conditions can be recast in a striking way completely in terms of explicit representation theoretic properties of the symmetric group (and the results improve upon the sufficient cohomological conditions established recently in the authors).