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Explore the foundational concepts of the Weil representation in this first lecture of a five-part mini-course series on Theta correspondences. Delve into various realizations of the Weil representation and gain a thorough understanding of the Metaplectic group definitions. Learn about the Weil index and its associated concepts through detailed mathematical discussions based on Gan-Kudla-Takada's book "The Local Theta Correspondence." Master key models of the Heisenberg Weil representation during this 85-minute mathematical exploration designed for advanced mathematics students and researchers.
