Character formulas and Bernstein-Gelfand-Gelfand resolutions for Cherednik algebra modules
Stephen Griffeth, Emily Norton
TL;DR
This paper investigates specific blocks of category O for Cherednik algebras where all irreducible modules have BGG resolutions, leading to a proven character formula conjectured by Oblomkov-Yun.
Contribution
It establishes the existence of BGG resolutions for all irreducible modules in certain Cherednik algebra blocks and proves a related character formula.
Findings
Proved a character formula conjectured by Oblomkov-Yun.
Identified conditions under which all irreducible modules admit BGG resolutions.
Enhanced understanding of the structure of category O for Cherednik algebras.
Abstract
We study blocks of category O for the Cherednik algebra having the property that every irreducible module in the block admits a BGG resolution, and as a consequence prove a character formula conjectured by Oblomkov-Yun.
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