I had understood that they were "Red Hat" or Mahayani.
I stand corrected, they are Geluk.
Tibetan Buddhism has five main schools (the suffix pa means sect):
Nyingma(pa), The Ancient Ones, the oldest and original school founded by Padmasambhava himself
Kadam(pa) (no longer existent although efforts to revitalize it are present in the Buddhist community)
Kagyu(pa), Oral Lineage, headed by the Karmapa
Sakya(pa), Grey Earth
Geluk(pa), Way of Virtue, also known as Yellow Hats, whose spiritual head is the Ganden Tripa and whose temporal head is the Dalai Lama, who was ruler of Tibet from the mid-17th to mid-20th centuries.