Detailed analysis of Duke Senior's character?
I can help you out with the basics for your request, but to do a detailed analysis, you need to carefully read As You Like It and come to your own conclusions about Duke Senior, based on what the play shows you. When you read or watch a play, you become part of the meaning of that play. A play needs an audience to appreciate and interpret it. So, what is most important in any character analysis, no matter what the play, is your take on the character, but here are some hints.
Think about how Senior acts when his brother comes in and deposes him, sending him out into the forest to live with those of his court who are inclined to follow him. Does he end up alone? No, his followers want to be with him, so they decide to endure a harsher life to stay at his side. What does this tell you about his character? For one, it means that he must be a good leader. Otherwise, his people would have stayed at court. It must mean that he commands respect, and it might mean that his people actually like him.
When you see him later in the play, holding court in the forest, it is clear that he cares for his people - another important aspect of his character. It is also clear that he loves his daughter. He did not command her to accompany him, because he knew that she was attached to her cousin and best friend, Celia.
And, at the end of the play, you know that he is manganimous, because he doesn't try to get even with his brother. So, just by reading or watching the play, you can determine the kind of character that Duke Senior possesses.