Definition cfDet_order_lin xi :
xi \is a linear_char -> cfDet_order xi = #[xi]%CF.

Lemma cfDet_mul_lin gT (G : {group gT}) (lambda phi : 'CF(G)) :
lambda \is a linear_char -> phi \is a character ->
cfDet (lambda * phi) = lambda ^+ truncC (phi 1%g) * cfDet phi.