Shigeo Koshitani

activity

20092026

p

-blocks with small numbers of characters

8 citations · 31 across the 22 of their papers we have counts for

collaborators

30 papers

math.RT2026

Reciprocity for projective and injective direct summands

Shigeo Koshitani, Taro Sakurai

A reciprocity between multiplicities of projective direct summands for modular group algebras has been known for decades. Recently, the first author extended it to finite-dimension…

math.RT2026

The Mathieu group $M_{12}$ vs $S L_{3} (3)$ in characteristic 3

Shigeo Koshitani, Tetsuro Okuyama

We prove that the principal $3$ -blocks of the Mathieu group $M_{12}$ and the special linear group $\SL_3(3)$ are splendidly Rickard equivalent, and hence derived equivalent,…

math.RT2026

A reciprocity theorem of Robinson-Benson-Webb for finite-dimensional symmetric algebras

Shigeo Koshitani

We generalize the reciprocity theorem of G.R.~Robinson, D. Benson and P. Webb between a finite group and its subgroup to the case of finite-dimensional {\it symmetric} algebras ove…

math.RT2024

Lifting Brauer indecomposability of a Scott module

Shigeo Koshitani, İpek Tuvay

It is proven that if a finite group $G$ has a normal subgroup $H$ with $p^{'}$ -index (where $p$ is a prime) and $G / H$ is solvable, then for a $p$ -subgroup $P$ of $H$ , if the Scott $kH…

math.RT2023

Principal 2-blocks with wreathed defect groups up to splendid Morita equivalence

Shigeo Koshitani, Caroline Lassueur, Benjamin Sambale

We classify principal $2$ -blocks of finite groups $G$ with Sylow $2$ -subgroups isomorphic to a wreathed $2$ -group $C_{2^{n}} ≀ C_{2}$ with $n \geq 2$ up to Morita equivalence and up to…

math.RT2022

Recognition of Brauer indecomposability for a Scott module

Shigeo Koshitani, İpek Tuvay

We give a handy way to have a situation that the $k G$ -Scott module with vertex $P$ remains indecomposable under taking the Brauer construction for any subgroup $Q$ of $P$ as $k[Q\,…

math.RT2020★ 3 cited

The Brauer indecomposability of Scott modules with wreathed $2$ -group vertices

Shigeo Koshitani, İpek Tuvay

We give a sufficient condition for the $k G$ -Scott module with vertex $P$ to remain indecomposable under taking the Brauer construction for any subgroup $Q$ of $P$ as $k [Q C_{G} (Q)]$ …

math.RT2020

Splendid Morita equivalences for principal blocks with semidihedral defect groups

Shigeo Koshitani, Caroline Lassueur, Benjamin Sambale

We classify principal blocks of finite groups with semidihedral defect groups up to splendid Morita equivalence. This completes the classification of all principal $2$ -blocks of ta…

math.RT2020

Trivial source endo-trivial modules for finite groups with a semi-dihedral Sylow $2$ -subgroup

Shigeo Koshitani, Caroline Lassueur

We finish off the classification of the endo-trivial modules of finite groups with Sylow $2$ -subgroups isomorphic to a semi-dihedral $2$ -group started by Carlson, Mazza and Thévena…

math.RT2020

Trivial source characters in blocks with cyclic defect groups

Shigeo Koshitani, Caroline Lassueur

We describe the ordinary characters of trivial source modules lying in blocks with cyclic defect groups relying on their recent classification in terms of paths on the Brauer tree…

math.RT2020★ 8 cited

The principal $p$ -blocks with small numbers of characters

Shigeo Koshitani, Taro Sakurai

For a prime $p$ , we determine a Sylow $p$ -subgroup $D$ of a finite group $G$ such that the principal $p$ -block $B$ of $G$ has four irreducible ordinary characters. It has been dete…

math.RT2019★ 4 cited

The Brauer indecomposability of Scott modules with semidihedral vertex

Shigeo Koshitani, İpek Tuvay

We present a sufficient condition for the $k G$ -Scott module with vertex $P$ to remain indecomposable under the Brauer construction for any subgroup $Q$ of $P$ as $k [Q C_{G} (Q)]$ -mod…

math.RT2018

Splendid Morita equivalences for principal blocks with generalised quaternion defect groups

Shigeo Koshitani, Caroline Lassueur

We prove that splendid Morita equivalences between principal blocks of finite groups with dihedral Sylow $2$ -subgroups realised by Scott modules can be lifted to splendid Morita eq…

math.RT2018

On theorems of Brauer-Nesbitt and Brandt for characterizations of small block algebras

Shigeo Koshitani, Taro Sakurai

In 1941, Brauer-Nesbitt established a characterization of a block with trivial defect group as a block $B$ with $k (B) = 1$ where $k (B)$ is the number of irreducible ordinary charac…

math.RT2017

Splendid Morita equivalences for principal 2-blocks with dihedral defect groups

Shigeo Koshitani, Caroline Lassueur

Given a dihedral $2$ -group $P$ of order at least~8, we classify the splendid Morita equivalence classes of principal $2$ -blocks with defect groups isomorphic to $P$ . To this end we…

math.RT2017★ 4 cited

The Brauer indecomposability of Scott modules and the quadratic group Qd(p)

Shigeo Koshitani, İpek Tuvay

Let $k$ be an algebraically closed field of prime characteristic $p$ and $P$ a finite $p$ -group. We compute the Scott $k G$ -module with vertex $P$ when $F$ is a constraine…

math.RT2017★ 2 cited

Simple modules in the Auslander-Reiten quiver of principal blocks with abelian defect groups

Shigeo Koshitani, Caroline Lassueur

Given an odd prime $p$ , we investigate the position of simple modules in the stable Auslander-Reiten quiver of the principal block of a finite group with non-cyclic abelian Sylow $…

math.RT2016

The projective cover of the trivial representation for a finite group of Lie type in defining characteristic

Shigeo Koshitani, Jürgen Müller

We give a lower bound of the Loewy length of the projective cover of the trivial module for the group algebra $k G$ of a finite group $G$ of Lie type defined over a finite field of…

math.RT2015

On the Brauer indecomposability of Scott modules

Radha Kessar, Shigeo Koshitani, Markus Linckelmann

Let $k$ be an algebraically closed field of prime characteristic $p$ , and let $P$ be a $p$ -subgroup of a finite group $G$ . We give sufficient conditions for the $k G$ -Scott module $…

math.RT2015

Endo-trivial modules for finite groups with dihedral Sylow 2-subgroup

Shigeo Koshitani, Caroline Lassueur

Let $k$ be an algebraically closed field of characteristic $p > 0$ and $G$ a finite group. We provide a description of the torsion subgroup $T T (G)$ of the finitely generated abelian…

math.GR2013

On symmetric quotients of symmetric algebras

Radha Kessar, Shigeo Koshitani, Markus Linckelmann

We investigate symmetric quotient algebras of symmetric algebras, with an emphasis on finite group algebras over a complete discrete valuation ring $O$ . Using elementary…

math.GR2013★ 7 cited

The inductive Alperin-McKay and blockwise Alperin weight conditions for blocks with cyclic defect groups

Shigeo Koshitani, Britta Spaeth

We verify the inductive blockwise Alperin weight (BAW) and the inductive Alperin-McKay (AM) conditions introduced by the second author for blocks of finite quasisimple groups with…

math.GR2013★ 1 cited

Clifford theory of characters in induced blocks

Shigeo Koshitani, Britta Spaeth

We present a new criterion to predict if a character of a finite group extends. Let $G$ be a finite group and $p$ a prime. For $N ⊲ G$ , we consider $p$ -blocks $b$ and $b^{'}$ of $N$ …

math.RT2013

Endo-trivial modules for finite groups with Klein-four Sylow 2-subgroups

Shigeo Koshitani, Caroline Lassueur

We study the finitely generated abelian group $T (G)$ of endo-trivial $k G$ -modules where $k G$ is the group algebra of a finite group $G$ over a field of characteristic $p > 0$ . When t…

Reciprocity for projective and injective direct summands

The Mathieu group M12​ vs SL3​(3) in characteristic 3

A reciprocity theorem of Robinson-Benson-Webb for finite-dimensional symmetric algebras

Lifting Brauer indecomposability of a Scott module

Principal 2-blocks with wreathed defect groups up to splendid Morita equivalence

Recognition of Brauer indecomposability for a Scott module

The Brauer indecomposability of Scott modules with wreathed 2-group vertices

Splendid Morita equivalences for principal blocks with semidihedral defect groups

Trivial source endo-trivial modules for finite groups with a semi-dihedral Sylow 2-subgroup

Trivial source characters in blocks with cyclic defect groups

The principal p-blocks with small numbers of characters

The Brauer indecomposability of Scott modules with semidihedral vertex

Splendid Morita equivalences for principal blocks with generalised quaternion defect groups

On theorems of Brauer-Nesbitt and Brandt for characterizations of small block algebras

Splendid Morita equivalences for principal 2-blocks with dihedral defect groups

The Brauer indecomposability of Scott modules and the quadratic group Qd(p)

Simple modules in the Auslander-Reiten quiver of principal blocks with abelian defect groups

The projective cover of the trivial representation for a finite group of Lie type in defining characteristic

On the Brauer indecomposability of Scott modules

Endo-trivial modules for finite groups with dihedral Sylow 2-subgroup

On symmetric quotients of symmetric algebras

The inductive Alperin-McKay and blockwise Alperin weight conditions for blocks with cyclic defect groups

Clifford theory of characters in induced blocks

Endo-trivial modules for finite groups with Klein-four Sylow 2-subgroups

The Mathieu group $M_{12}$ vs $S L_{3} (3)$ in characteristic 3

The Brauer indecomposability of Scott modules with wreathed $2$ -group vertices

Trivial source endo-trivial modules for finite groups with a semi-dihedral Sylow $2$ -subgroup

The principal $p$ -blocks with small numbers of characters