(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>
 
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Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Yaeli Malka   <yaeli.malka@weizmann.ac.il>