One of those aspects is architecture. Lotus is a very outstanding and holy motif in Indian culture. You must have seen pictures of the statues of Gautama Buddha in which he is shown sitting on lotus. Sometimes Shiva and Krishna are shown in the same position. It has its roots in the old legends and myths, going back to Brahma. When the Muslims settled in India, they brought dome and minaret from Middle East and Turkey. But the domes built by them in the early periods were, like those of the Middle East, simplistic in design.
Then the process of mutual give-and-take began, until we come to the ultimate poetry in marble, which is known as Taj Mahal, pictures of which you must have seen everywhere. If you study the upper section of its dome, you will see that the architects have capped it with inverted lotus. Thus by combining the Muslim dome and Hindu lotus, they have created the master-piece of Indian architecture, which is rightfully called the eighth wonder of the world.
We also find many features and designs in Muslim buildings in India which show the influence of the ancient culture that was prevalent in India.