Nellie, you're right. Those robes (purple velvet, edged with ermine and bordered with gold lace) are worn by Princesses of the United Kingdom. They are worn at Coronations. The only other 20th century occasion when they made an appearance was at the 1911 Delhi Durbar, when they were worn by the Emperor and Empress (no other members of the Royal Family being present).

The robe and cape are as one, sewn at the neck hem. With a lady, where the robe hangs from the shoulders, the gold bullion ropes and tassels are purely ornamental. Any white silk-satin ribbons are employed to secure chivalric chains.

All ladies' robes are fastened by the same principle: strips extending from the neck hem, generally covered in ermine to camouflage them, that pass under the arms and employ a hook-and-eye device to attach near the top on the underside of the robe. This photograph of The Queen, wearing her crimson robe at the State Opening of Parliament, illustrates what I mean.