Symbols are objects, characters, figures, and colors used to represent abstract ideas or concepts.
The ridiculous outfit Petruchio wears to his wedding with Kate symbolizes his control over her. Simply by wearing the costume, he is able to humiliate her. It may be shameful for Kate to be matched to someone in such attire, but she knows she has no choice if she does not wish to become an old maid. She consents to let the ceremony proceed, even with Petruchio dressed like a clown, and thus yields to his authority before the wedding even begins.
The outfit also symbolizes the transient nature of clothing. Petruchio declares that Kate is marrying him, not his clothes, indicating that the man beneath the attire is not the same as the attire itself. Thus, Lucentio, dressed as a tutor, cannot escape the fact that he must return to his true identity. By the same token, when Kate plays the role of a dutiful wife, she remains, essentially, Kate.
The cap and gown that Petruchio denies Katherine, despite the fact that she finds them truly appealing, symbolizes yet again his power over her. The outfit functions as a kind of bait used to help convince Kate to recognize and comply with Petruchio’s wishes. Only he has the power to satisfy her needs and desires, and this lesson encourages her to satisfy him in return.