The Imprimitive Faithful Complex Characters of the Schur Covers of the Symmetric and Alternating Groups

2008/12/19 by Daniel Nett, Nett, Daniel, Felix Noeske +1
Computer Science · Mathematics · #Coding theory and cryptography #Finite Group Theory Research #Geometric and Algebraic Topology #math.GR #math.RT #msc:20B35 #msc:20C15 #msc:20E28

paper · pdf · doi:10.48550/arxiv.0812.3746

19 pages

arxiv created 2008/12/19 · arxiv updated 2009/12/01

Abstract

Using combinatorics and character theory, we determine the imprimitive faithful complex characters, i.e., the irreducible faithful complex characters which are induced from proper subgroups, of the Schur covers of the symmetric and alternating groups. Furthermore, for every imprimitive character we establish all its minimal block stabilizers. As a corollary, we also determine the monomial faithful characters of the Schur covers.

Related

• Character correspondences above fully ramified sections and Schur indices
• Character Theory and Categorification
• Covering Numbers of Some Irreducible Characters of the Symmetric Group
• Characters and projective characters of alternating and symmetric groups determined by values on l'-classes
• A conjectured combinatorial interpretation of the normalized irreducible character values of the symmetric group