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.
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Ko, H.J., Lee, K.J. Intertwining numbers; The n-rowed shapes. Czech Math J 57, 53–66 (2007). https://doi.org/10.1007/s10587-007-0043-y
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DOI: https://doi.org/10.1007/s10587-007-0043-y