What are the specific historical influences or elements from the Byzantine era shown in the photo from the Dolce & Gabbana Fall 2013 ready-to-wear collection?
Clothing of the Byzantine era was very modest in cover. Both men and women were covered from neck to feet. This complete covering was due to the Christian influence. The people of this period desired their clothing to exhibit their modesty.
That said, their modesty ended with the complete covering of their bodies. The fabrics of this period were elaborate. Gold and silver fibers were woven into rich (silk) fabrics. The people also beaded their fabrics. Another thing they highly prized was color. Although purple was left for royals, all other colors were open for the people. Merchants would search as far as possible to find the best dyes.
There are two elements from the Byzantine period seen in the D&G collection above. The heavy beading and color. Outside of that, neither the length of sleeves or hemline reflect the Byzantine period.