Abstract
A fairly old problem in modular representation theory is to determine the vanishing behavior of the Hom groups and higher Ext groups of Weyl modules and to compute the dimension of the ℤ/(p)-vector space $$Hom_{\bar A_r } (\bar K_\lambda ,\bar K_\mu )$$ for any partitions λ, μ of r, which is the intertwining number. K. Akin, D. A. Buchsbaum, and D. Flores solved this problem in the cases of partitions of length two and three. In this paper, we describe the vanishing behavior of the groups $$Hom_{\bar A_r } (\bar K_\lambda ,\bar K_\mu )$$ and provide a new formula for the intertwining number for any n-rowed partition.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: 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.