A pelisse is a jacket worn on one shoulder like a cloak.
Essentially it is a short, and when worn extremely tight fitting, jacket trimmed with fur. It is attached by draping over the left shoulder and clasping a cord across the body. This is diagonal from the left collar of the pelisse, across the chest, under the right arm and clasped to the right collar of the pelisse at the back.
Ostensibly to protect cavalry troopers from Sword cuts it was originally used by Hungarian mercenaries in the 17th century but as the style and tactics of other European armies became fashionable so did the clothing, the pelisse becoming common in Europe, and to a lesser degree in the Americas, by the 19th century.