For those of you who don't read the books, I'll try to give a quick description without hopefully spoiling anything for you, but please read at your own peril...
House Martell is one of the many great families of Westeros. They have kept their ruling title of "Prince" and "Princess" from never being beaten in battle. They only joined the Seven Kingdoms through royal marriage. Their House motto is, "Unbowed, Unbent, Unbroken".
Arianne Martell (23 years old) is the eldest daughter of Prince Doran, ruler of Dorne. Niece to Oberyn Martell (the Red Viper). She is first in line to succeed her father in ruling Dorne (Dorne recognizes male and female heirs, unlike the rest of Westeros. Making it a definitely unique place.)
Arianne is one of my favorite characters based on how head strong she is. She truly is groomed to be a ruler, albeit she makes a few errors along the way, due to a few misunderstandings with her father. She has a very strong sexual prowess that is empowering. In many ways she is considered more like her Uncle Oberyn than her father, and her personality truly represents her house motto.
Now to a few casting choices!
Arianne is short 5'2", curvy, dark eye'd, long curly hair, and thick lips. Pretty much an exotic beauty. I kind of think of Princess Jasmine in an R-rated way when I think of Arianne. So based on that theory here's just a few who "could" pull it off.
1. Janina Gavankar
She's a fantastic actress and not new to T.V. series. She's not afraid to get naked on television either, and with Arianne being the kind of girl who is not afraid to seduce men to do her bidding...We kind of need that. (see True Blood, which is also an HBO show)!
2. Lindsey Morgan
She's young (Arianne is only 23 in the books). She plays Raven on the new hit series, The 100, and does a fantastic job playing a independent, head strong female. And damn she is really fit.
3. Francia Raisa
She's also a veteran of T.V. series, though it was The Sercret Life of the American Teenager, we've seen Shailene Woodley branch out and do fantastic. I'm sure this beautiful lady will too.
4. Gemma Arterton
No one can deny she's beautiful. She played a pretty kick ass lady in Hansel and Gretel. Though she's a bit paler than I imagine Arianne to be, she did tan well for Prince of Persia, I think she'd do fine.
5. Freida Pinto
She played along side Henry Cavill in the Immortals. She also starred in Rise of the Planet of the Apes.
6. Rima Fakih
Most of her "acting" gigs have been guest appearances and such, but I bet this girl has some acting lesson up her sleeve. One thing I do know, she looks perfect for the role.