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Let H n,r be the Ariki-Koike algebra associated to the complex reflection group S n ⋉ (Z/rZ) n , and S(Λ) be the cyclotomic q-Schur algebra associated g >0 such that r 1 + · · · + r g = r, we define a subalgebra S p of S(Λ) and its quotient algebra S p. It is shown that S p is a standardly based algebra and S p is a cellular algebra. By making use of these(More)
In this paper, we prove Lusztig's conjecture for G F = SL n (F q), i.e., we show that characteristic functions of character sheaves of G F coincide with almost characters of G F up to scalar constants, assuming that the characteristic of F q is not too small. We determine these scalars explicitly. Our result gives a method of computing irreducible(More)
This paper is concerned with the problem of the determination of unknown scalars involved in the algorithm of computing the generalized Green functions of reductive groups G over a finite field. In the previous paper, we have treated the case where G = SL n. In this paper, we determine the scalars in the case where G is a classical group Sp 2n or SO N for(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 Sp 2n (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 Sp 2n (Fq) with p =(More)
Let H n,r be the Ariki-Koike algebra associated to the complex reflection group S n (Z/rZ) n , and let S(Λ) be the cyclotomic q-Schur algebra associated to H n,r , introduced by Dipper, James and Mathas. For each p = (r 1 ,. .. , r g) ∈ Z g >0 such that r 1 + · · · + r g = r, we define a subalgebra S p of S(Λ) and its quotient algebra S p. It is shown that(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 sp 2n over C, that over characteristic two, and our exotic Springer correspondence. As a by-product, we obtain a complete description of our exotic(More)