Category decomposition of Repk(SLn(F))
Abstract
Let F be a non-archimedean local field with residual characteristic p, and k an algebraically closed field of characteristic l different from p. We establish a category decomposition of Repk(SLn(F) according to the GLn(F)-inertially equivalent supercuspidal classes of SLn(F), and we give a block decomposition of the supercuspidal sub-category of Repk(SLn(F)). Finally we give an example to show that in general a block of SLn(F) is not defined according to a unique inertially equivalent supercuspidal classes of SLn(F), which is different from the case when l=0.
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