Toshiaki Shoji

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In this paper, we prove Lusztig’s conjecture for GF = SLn(Fq), i.e., we show that characteristic functions of character sheaves of GF coincide with almost characters of GF up to scalar constants, assuming that the characteristic of Fq is not too small. We determine these scalars explicitly. Our result gives a method of computing irreducible characters of GF(More)
Let G = Sp (2n) be the symplectic group over Z. We present a certain kind of deformation of the nilpotent cone of G with G-action. This enables us to make direct links between the Springer correspondence of sp2n over C, that over characteristic two, and our exotic Springer correspondence. As a by-product, we obtain a complete description of our exotic(More)
An irreducible ordinary character of a finite reductive group is called quadratic unipotent if it corresponds under Jordan decomposition to a semisimple element s in a dual group such that s = 1. We prove that there is a bijection between, on the one hand the set of quadratic unipotent characters of GL(n, q) or U(n, q) for all n ≥ 0 and on the other hand,(More)
The determination of scalars involved in Lusztig’s conjecture concerning the characters of finite reductive groups was achieved by Waldspurger in the case of finite classical groups Sp2n(Fq) or On(Fq) when p, q are large enough. Here p is the characteristic of the finite field Fq . In this paper, we determine the scalars in the case of Sp2n(Fq) with p = 2,(More)