A note on Hecke patterns in Category O
Rahbar Virk
TL;DR
This paper investigates how derived auto-equivalences in category O relate to Hecke algebra generators, exploring both graded and ungraded contexts to deepen understanding of their algebraic structure.
Contribution
It introduces a new perspective on the connection between auto-equivalences in category O and Hecke algebra generators, extending previous work to both graded and ungraded cases.
Findings
Established a correspondence between auto-equivalences and Hecke algebra generators.
Analyzed the differences between graded and ungraded scenarios.
Provided new insights into the structure of derived auto-equivalences in category O.
Abstract
We study the family of derived auto-equivalences of the BGG-category O that correspond to the action of the standard generators of the Hecke algebra. Both the non-graded and graded situations are considered.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Homotopy and Cohomology in Algebraic Topology