Ayeka is the crowned princess of Jurai. After Yosho's disappearance Ayeka was next in line for the throne. She had been learning all her life the customs and laws of Jurain royalty. She is polite and proper unlike her chief rival for Tenchi's affections, Ryoko. Of the two girls I feel that Ayeka is better for Tenchi. But Ryoko would be more fun. Despite her proper outer visage she has a dark side.
Ayeka has two guardians that may not be physically with her at all times can be summoned whenever she needs them. The guardians have been the protectors of the highest ranked Jurain royalty since ancient times. In the TV series they served as storage facilities for the essences of the Knights of Jurai.
Other than controlling the two guardians Ayeka can summon lesser versions of Azaka and Kamidake. These lesser versions are not intelligent like Azaka and Kamidake. They emit powerful force fields which can be used for both offense and defense. They can also be used to contain other people and objects. Once they've engaged their force field Ayeka can move them and whatever they contain wherever she wants. Being a member of the Royal family she has the ability to control Jurai power. She channels it through the tiara on her head in much the same way Tenchi uses the sword. She can then channel it into laser blasts.
In the OAV the Ayeka's tiara also served as the control device for her tree of Jurai. Jurain keys are created on the tree which they will control. The key takes a form to suit its new owner. Sword Tenchi is from Tsunami and therefore can control all Jurain ships and override their owners' keys. This happened in OAV 2 when Ryoko smashed Ryu-Oh into Earth.
Ryu-Oh, Ayeka's ship crashed into Earth in OAV 2 after that it couldn't fly. Ryo-Ohki raised it from the lake and took it into space to fight Soja. There Ryu-Oh was completely destroyed. All that remained was a seed which Ayeka planted in the Jurian shell that they took from Kagato. Take a good look at it on the right because one way or another it spends most of its time at the bottom of the lake. That shell was built for Tsunami, but it suited their purposes. In the TV series, Ryu-Oh still crashed into the Earth but the tree rooted itself into the middle of the lake and began to grow. But once Jurain trees get roots in soil they lose their powers.
Ayeka's father is Azusa, King of Jurai. Her mother is Misaki, the mentally unstable queen of Jurai. She also has a younger sister Sasami. Sasami is another of the major characters in this series.