Mathematical Sciences: Representation Theory and            Differential Geometry
{'Code': '03040108', 'Directorate': {'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'James Glazebrook'}
Bertram Kostant will continue his research in the theory of                Lie groups. The work will proceed in three directions 1) a plan                 for carrying out geometric quantization of certain nilpotent                    orbits by use of quasi-invariant differential operators; 2) an                  approach to determine generalized exponents by the use of special               Kazhdan-Lusztig polynomials in the affine case and new                          information on the equivariant K-theory of the corresponding                    infinite dimensional flag manifold; 3) an approach to establish                 the positive definiteness of the Hermitian structure on the space               of physical states.                                                                  The determination of representations whose wave front set is               the closure of the Joseph orbit is an important and difficult                   problem. These representations are generalizations of the                       oscillator representation for the two fold covering of the                      symplectic group. The study of the Kazhdan-Lusztig polynomials                  for Lie groups associated with affine Lie algebras using geometry               of the corresponding flag variety and its relationship with K-                  theory is a very important aspect of this research.
{'FirstName': 'Bertram', 'LastName': 'Kostant', 'EmailAddress': 'kostant@math.mit.edu', 'StartDate': '07/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Massachusetts Institute of Technology', 'CityName': 'Cambridge', 'ZipCode': '021394301', 'PhoneNumber': '6172531000', 'StreetAddress': '77 MASSACHUSETTS AVE', 'CountryName': 'United States', 'StateName': 'Massachusetts', 'StateCode': 'MA'}
[{'Code': '1262', 'Text': 'MODERN ANALYSIS'}, {'Code': '1265', 'Text': 'GEOMETRIC ANALYSIS'}]
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8703278.xml'}