(The previously announced title for this talk has been changed.) The Weizmann Institute of Science Faculty of Mathematics and Computer Science Algebraic Geometry and Representation Theory Seminar Seminar Room, Room 261, Ziskind Building on Monday, June 11, 2012 11:00 - 12:30 Siddhartha Sahi Rutgers University, USA will speak on The Capelli identity for Grassmannians Abstract: The classical Capelli identity [1887] is a certain identity of differential operators on the space of n x n matrices. It played a crucial role in Herman Weyl's approach to 19th century invariant theory and has continued to find modern day applications, e.g. in the work of Atiyah-Bott-Patodi on the index theorem. In the early 1990s the identity was reinterpreted by Kostant and the speaker, as an eigenvalue problem for a certain invariant differential operator, and generalized to the setting of Jordan algebras. Let Gr(n,k) denote the Grassmannian of k-planes in n-space. In recent work, Howe-Lee solve an analogous Capelli type eigenvalue problem for differential operators on Gr(n,2). Their method is elementary but involves fairly intricate computations, and it is not clear how to extend this to other cases. In this talk we explain how to solve the problem for all k using ideas from representation theory. <http://www.math.rutgers.edu/~sahi/Preprints/Capelli4-18.pdf> --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Yaeli Malka <yaeli.malka@weizmann.ac.il>