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- TOSHIAKI SHOJI, T. SHOJI
- 2001

Green functions associated to complex reflection groups G(e, 1, n) were discussed in the author's previous paper. In this paper, we consider the case of complex reflection groups W = G(e, p, n). Schur functions and Hall-Littlewood functions associated to W are introduced, and Green functions are described as the transition matrix between those two symmetric… (More)

- Toshiaki Shoji
- 2008

Let G be a simple algebraic group over C with the Weyl group W. For a unipotent element u ∈ G, let B u be the variety of Borel subgroups of G containing u. Let L be a Levi subgroup of a parabolic subgroup of G with the Weyl subgroup W L of W. Assume that u ∈ L and let B L u be a similar variety as B u for L. For a certain choice of L, u ∈ L and e ≥ 1, we… (More)

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)

- TOSHIAKI SHOJI, Noriaki Kawanaka
- 2005

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)

- TOSHIAKI SHOJI
- 2005

The algorithm of computing generalized Green functions of a reduc-tive group G contains some unknown scalars occurring from the F q-structure of irreducible local systems on unipotent classes of G. In this paper, we determine such scalars in the case where G = SL n with Frobenius map F of split type or non-split type. In the case where F is of non-split… (More)

- TOSHIAKI SHOJI
- 2006

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)

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)

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 W be the complex reflection group S n ⋉ (Z/eZ) n. In the author's previous paper [S1], Hall-Littlewood functions associated to W were introduced. In the special case where W is a Weyl group of type B n , they are closely related to Green polynomials of finite classical groups. In this paper, we introduce a two variables version of the above… (More)