Rigidity of tilting modules in category O
Kevin Coulembier
TL;DR
This paper reviews the known rigidity properties and Loewy lengths of tilting modules in category O for reductive Lie algebras, clarifying results that are well-known but not easily accessible in literature.
Contribution
It provides a comprehensive overview of the rigidity and Loewy length properties of tilting modules in category O, consolidating known results for easier reference.
Findings
Rigidity properties of tilting modules clarified
Loewy lengths of tilting modules characterized
Results compiled for accessibility
Abstract
In this note we give an overview of rigidity properties and Loewy lengths of tilting modules in the BGG category O associated to a reductive Lie algebra. These results are well-known by several specialists, but seem difficult to find in the existing literature.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology