Homological algebra and divergent series.
A fairly old problem in modular representation theory is to determine the vanishing behavior of the groups and higher groups of Weyl modules and to compute the dimension of the -vector space for any partitions , of , 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 and provide a new formula for the intertwining number for any...
Let be a commutative Noetherian ring. It is shown that the finitely generated -module with finite Gorenstein dimension is reflexive if and only if is reflexive for with , and for with . This gives a generalization of Serre and Samuel’s results on reflexive modules over a regular local ring and a generalization of a recent result due to Belshoff. In addition, for we give a characterization of -Gorenstein rings via Gorenstein dimension of the dual of modules. Finally it is shown...