The name of the square comes from the elm tree planted in the centre. The square formed part of the monastery site, but was not considered a strict enclosure as lay people could enter for different reasons. For example, in the northern side the provost’s main house, where the monk who exercised jurisdictional lordship over the village lived, to whom the subjects had to pay the ground rents, tithes and other taxes and was home to the mayor’s judicial court. Of this building, today only the lower part of the prison tower remains, which was as high as the main entrance tower.
In front of the square, in the east, is the Small Cloister, a late 16th century Renaissance construction. The building occupies the space formerly occupied by the Monastery’s porter’s lodge and where lodging was given to the poor and pilgrims in the 10th century. Today it is still the entrance to the Romanesque Cloister.
The southern side of the square is occupied by the former Abbot’s Palace, a building that today houses parish services.