Representations and primitive central idempotents of a finite solvable group

2018/10/09 by Ravi S. Kulkarni, Kulkarni, Ravi S., Soham Swadhin Pradhan +1
Mathematics · #FOS: Mathematics #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.1810.04166

arxiv created 2018/10/09 · arxiv updated 2018/10/11

Abstract

Let G be a finite solvable group. Then G always has a useful presentation, which we call a "long presentation". Using a "long presentation" of G, we present an inductive method of constructing the irreducible representations of G over ℂ and computing the primitive central idempotents of the complex group algebra ℂ[G]. For a finite abelian group, we present a systematic method of constructing the irreducible representations over a field of characteristic either 0 or prime to order of the group and also a systematic method of computing the primitive central idempotents of the semisimple abelian group algebra.

Related

• Algorithmic construction of representations of finite solvable groups
• Primitive Central Idempotents of the Group Algebra
• Primitive Central Idempotents of Rational Group Algebras
• Primitive Central idempotents and the Wedderburn Decomposition of a Rational Abelian Group Algebra
• Representations of finite groups