Relation between k and group velocity in bands

[hokhani]

In transitions in the crystals we always use conservation of wave vector of electron, not electron momentum conservation. For example in an indirect transition from top of valence band to bottom of conduction band, the group velocity of electron and hence its momentum would not change (it is zero at the two points). so why do we need a phonon to conserve the momentum?

 

[DrDu]

Because of conservation of the crystal momentum aka wavevector? Note that the crystal momentum is distinct from the true momentum of the particle.