Determinants of Representations of Coxeter Groups

2017/10/09 by Ghosh, Debarun, Spallone, Steven · 1 citation
#20C15 #20C30 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1710.03039

Abstract

In [APS], the authors characterize the partitions of n whose corresponding representations of S_n have nontrivial determinant. The present paper extends this work to all irreducible finite Coxeter groups W. Namely, given a nontrivial multiplicative character ω of W, we give a closed formula for the number of irreducible representations of W with determinant ω. For Coxeter groups of type B_n and D_n, this is accomplished by characterizing the bipartitions associated to such representations.

Cited by

• Enumeration of Even Dimensional Partitions modulo 4

Related

• On the determinant of representations of generalized symmetric groups
• Divisibility of Character Values of Representations of Coxeter Groups
• A Construction of Coxeter Group Representations (II)
• Projective Joint Spectra and Characters of representations of A_n
• Spectral analysis and representations]Spectral analysis near regular point of reducibility and representations of Coxeter groups