Mathematical Sciences: Analysis on Semisimple Groups
{'Code': '03040103', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'William Y. Velez', 'PO_EMAI': None, 'PO_PHON': None}
The principal investigator plans to work on problems in                    mathematical analysis concerning the representation theory of                   (semisimple) Lie groups.  A suitable example of the latter is the               group of rotations of a sphere.  Groups like this are important                 because they occur in many areas of mathematics ( e.g. geometry,                differential equations,algebraic number theory, mathematical                    physics ) as groups of symmetries.  Representation theory allows                one to take advantage of symmetries in solving problems.                             The building blocks for representation theory are                          the irreducible representations, particularly the irreducible                   unitary representations.  The principal investigator will work                  toward classifying these representations for semisimple Lie                     groups.  Prior work provides a considerable store of examples and               techniques for attacking this problem, which in the indicated                   degree of generality is very hard, and absolutely central to                    the subject.  Some common themes have emerged and some subtle                   critical cases have appeared.  The plan is to pursue the common                 themes and concentrate on the role played by generalizations of                 the critical cases.
{'FirstName': 'Anthony', 'LastName': 'Knapp', 'PI_MID_INIT': 'W', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Anthony W Knapp', 'EmailAddress': None, 'NSF_ID': '000228716', 'StartDate': '04/15/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'SUNY at Stony Brook', 'CityName': 'STONY BROOK', 'ZipCode': '117940001', 'PhoneNumber': '6316329949', 'StreetAddress': 'W5510 FRANKS MELVILLE MEMORIAL L', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'New York', 'StateCode': 'NY', 'CONGRESSDISTRICT': '01', 'CONGRESS_DISTRICT_ORG': 'NY01', 'ORG_UEI_NUM': 'M746VC6XMNH9', 'ORG_LGL_BUS_NAME': 'THE RESEARCH FOUNDATION FOR THE STATE UNIVERSITY OF NEW YORK', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '1262', 'Text': 'MODERN ANALYSIS'}
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