#### Filter Results:

- Full text PDF available (11)

#### Publication Year

1973

2012

- This year (0)
- Last 5 years (1)
- Last 10 years (6)

#### Publication Type

#### Co-author

#### Journals and Conferences

#### Key Phrases

Learn More

- 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 Bu 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 WL of W . Assume that u ∈ L and let B L u be a similar variety as Bu for L. For a certain choice of L, u ∈ L and e ≥ 1, we… (More)

- TOSHIAKI SHOJI
- 2005

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

- Toshiaki Shoji
- Applicable Algebra in Engineering, Communication…
- 1996

We determine the constants appearing in the Lusztig conjecture in the case of unipotent characters of classical groupsG subject to the condition that the characteristic is odd and the center ofG is connected. This enables us to compute the character values of unipotent characters of such finite classical groups.

- TOSHIAKI SHOJI, Noriaki Kawanaka
- 2005

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)

- T Shoji
- [Kango kyōiku] Japanese journal of nurses…
- 1973

Let Hn,r be the Ariki-Koike algebra associated to the complex reflection group Sn (Z/rZ)n, and let S(Λ) be the cyclotomic q-Schur algebra associated to Hn,r, introduced by Dipper, James and Mathas. For each p = (r1, . . . , rg) ∈ Zg>0 such that r1 + · · · + rg = r, we define a subalgebra Sp of S(Λ) and its quotient algebra S. It is shown that Sp is a… (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)