Isotypic blocks are functorially equivalent

TL;DR

This paper proves that isotypic blocks of finite groups are functorially equivalent over an algebraically closed field of characteristic zero, revealing a fundamental structural similarity.

Contribution

It establishes the functorial equivalence of isotypic blocks of finite groups over algebraically closed fields of characteristic zero, a new insight in modular representation theory.

Findings

Isotypic blocks are functorially equivalent over .

The result applies to finite groups in characteristic zero.

Provides a new perspective on block theory in representation theory.

Abstract

Let $\mathbb{F}$ be an algebraically closed field of characteristic zero. In this article we show that isotypic blocks of finite groups are functorially equivalent over $\mathbb{F}$.