Borel and shifted category O
David Hernandez, Andrei Negu\c{t}
TL;DR
This paper establishes a detailed relationship between simple modules in the Borel category O and the shifted category O for symmetrizable Kac-Moody Lie algebras, enhancing understanding of their representation theory.
Contribution
It provides a precise mathematical link between two important categories of modules in Kac-Moody algebra representation theory, which was previously not well-understood.
Findings
Established a relation between simple modules in Borel and shifted categories O
Enhanced understanding of module structures in Kac-Moody Lie algebras
Potential implications for categorification and algebraic geometry
Abstract
We prove a precise relation between simple modules in the Borel category O and the shifted category O for a symmetrizable Kac-Moody Lie algebra.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Combinatorial Mathematics