Mathematical Sciences: The U-cohomology of Generalized VermaModules
{'Code': '03040103', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': None, 'PO_EMAI': None, 'PO_PHON': None}
The theory of Lie groups, named in honor of the Norwegian                    mathematician Sophus Lie, has been one of the major themes in                   twentieth century mathematics.  As the mathematical vehicle for                 exploiting the symmetries inherent in a system, Lie theory has                  had a profound impact upon mathematics itself and theoretical                   physics, especially quantum mechanics and elementary particle                   physics.  Critical to the use of Lie theory are the linear                      realizations of the symmetries, called representations.                            In recent years, the algebraic approach to representation                    theory of semi-simple Lie groups has grown in power and                         importance, and it dominates in the attempt to classify all the                 irreducible representations.  Professor Shelton is an expert in                 this methodology.  His work involves an array of interactions                   with other areas of mathematics, including homological algebra,                 spectral sequences, and sheaves of differential operators.  He                  has begun a systematic study of the difficult problem of                        computing extensions between universal highest weight modules in                various categories.  He has solved this problem for certain                     special classes of groups, most notably those associated to                     Hermitian symmetric pairs.  He proposes to extend his work to the               general category of semi-simple Lie groups.
{'FirstName': 'Brad', 'LastName': 'Shelton', 'PI_MID_INIT': 'S', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Brad S Shelton', 'EmailAddress': 'shelton@math.uoregon.edu', 'NSF_ID': '000423283', 'StartDate': '07/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Oregon Eugene', 'CityName': 'EUGENE', 'ZipCode': '974031905', 'PhoneNumber': '5413465131', 'StreetAddress': '1776 E 13TH AVE', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Oregon', 'StateCode': 'OR', 'CONGRESSDISTRICT': '04', 'CONGRESS_DISTRICT_ORG': 'OR04', 'ORG_UEI_NUM': 'Z3FGN9MF92U2', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF OREGON', 'ORG_PRNT_UEI_NUM': 'Z3FGN9MF92U2'}
{'Name': None, 'CityName': None, 'StateCode': None, 'ZipCode': None, 'StreetAddress': None, 'CountryCode': None, 'CountryName': None, 'StateName': None, 'CountryFlag': None, 'CONGRESSDISTRICT': None, 'CONGRESS_DISTRICT_PERF': '""'}
{'Code': '126200', 'Text': 'MODERN ANALYSIS'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8700985.xml'}