上海科技大学知识管理系统

For an inner form G of a general linear group or classical group over a non-archimedean local field of odd residue characteristic, we decompose the category of smooth representations on Z[ 1 / p, µpâ ]-modules by endo-parameter. We prove that parabolic induction preserves these decompositions, and hence that it preserves endo-parameters. Moreover, we show that the decomposition by endo-parameter is the Z[1/p]-block decomposition; and, for R an integral domain, introduce a graph whose connected components parameterize the R - blocks, in particular including the cases R = Zâ  and R = Fâ for â â   p . From our description, we deduce that the Zâ -blocks and Fâ -blocks of G are in natural bijection, as had long been expected. Our methods also apply to the trivial endo-parameter (i.e., the depth zero subcategory) of any connected reductive p -adic group, providing an alternative approach to results of Dat and Lanard in depth zero. Finally, under a technical assumption (known for inner forms of general linear groups) we reduce the R - block decomposition of G to depth zero.