Modular Reduction of the Steinberg Lattice of the General Linear Group Ii
نویسنده
چکیده
Let G = GLn(q) be the general linear group of degree n ≥ 2 defined over a finite field Fq of characteristic p. We fix a prime l 6= p and let stand R for a local principal ideal domain having characteristic 0, maximal ideal lR, and containing a primitive p-th root of unity. Then the residue field K = R/lR has characteristic l and a primitive p-th root of unity. By a Steinberg lattice of G over R we understand a left RG-module, say M , which is free of rank qn(n−1)/2 as an R-module and affords the Steinberg character. The reduction of M modulo l is the KG-module M/lM . In this paper the Steinberg lattice is the left ideal I = RG · e of the group algebra RG, where e ∈ RG is defined by e = ∑
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