LAUSR

In Ayyer et al. (J Comb Theory Ser A 150:208–232, 2017), the authors characterize the partitions of n whose corresponding representations of $$S_n$$Sn have nontrivial determinant. The present paper extends this work to all irreducible finite Coxeter groups W. Namely, given a nontrivial multiplicative character $$\omega $$ω of W, we give a closed formula for the number of irreducible representations of W with determinant $$\omega $$ω. For Coxeter groups of type $$B_n$$Bn and $$D_n$$Dn, this is accomplished by characterizing the bipartitions associated to such representations.