Abstract
We analyze the BGG Category O over a large class of generalized Weyl algebras (henceforth termed GWAs). Given such a “triangular” GWA for which Category O decomposes into a direct sum of subcategories, we study in detail the homological properties of blocks with finitely many simples. As consequences, we show that the endomorphism algebra of a projective generator of such a block is quasi-hereditary, finite-dimensional, and graded Koszul. We also classify all tilting modules in the block, as well as all submodules of all projective and tilting modules. Finally, we present a novel connection between blocks of triangular GWAs and Young tableaux, which provides a combinatorial interpretation of morphisms and extensions between objects of the block.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
