On Extensions Between Verma Modules
Kevin J. Carlin
TL;DR
This paper discusses recent advances in understanding the extensions between Verma modules, focusing on a specific conjecture and its implications for modules with regular integral highest weights.
Contribution
It highlights a recent result that confirms the Gabber-Joseph conjecture for first-degree extensions between certain Verma modules.
Findings
Gabber-Joseph conjecture verified for first-degree extensions
Extension properties for Verma modules with regular integral weights clarified
Implications for representation theory of Lie algebras
Abstract
A recent result of N. Abe implies that the Gabber-Joseph conjecture is true for the first-degree extensions between Verma modules with regular integral highest weights.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Algebraic Geometry and Number Theory