Mathematical Sciences: Schubert Varieties and Standard      Monomial Theory
{'Code': '03040300', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Ann K. Boyle', 'PO_EMAI': None, 'PO_PHON': None}
This research will concentrate on problems connected with a                 semi-simple, simply-connected algebraic group G over a field k,                 the Borel subgroup B of G and a Schubert variety  in the flag                   variety G/B.  The P.I. has developed a standard monomial theory                 as a generalization of the classical Hodge-Young standard                       monomial theory.  The following specific problems will be                       considered.  Determine the multiplicity of a singular point on a                Schubert variety.  Write down the equations of the conormal                     bundle of a Schubert variety.  Study the variety XY = YX = 0                    where X and Y are matrices.  Develope a standard monomial theory                for a Kac group associated to an indecomposable, symmetrizable,                 generalized Cartan matrix of affine type.                                            This research is in algebraic geometry, the study of the                   geometric objects (varieties) arising as solutions of systems of                polynomial equations.  The P.I. considers very concrete varieties               and asks for very explicit, combinatorial answers to them.  The                 types of varieties she considers are very important and the type                of answers she seeks are widely applicable.  Very important                     results will come out of this research.
{'FirstName': 'Venkatramani', 'LastName': 'Lakshmibai', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Venkatramani Lakshmibai', 'EmailAddress': 'lakshmibai@neu.edu', 'NSF_ID': '000237256', 'StartDate': '07/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Texas A&M Research Foundation', 'CityName': 'COLLEGE STATION', 'ZipCode': '778454375', 'PhoneNumber': '9798626777', 'StreetAddress': '400 HARVEY MITCHELL PKWY S STE 3', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Texas', 'StateCode': 'TX', 'CONGRESSDISTRICT': '10', 'CONGRESS_DISTRICT_ORG': 'TX10', 'ORG_UEI_NUM': 'EQH8NQ4AXFT7', 'ORG_LGL_BUS_NAME': 'TEXAS A & M RESEARCH FOUNDATION', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '126400', 'Text': 'ALGEBRA,NUMBER THEORY,AND COM'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8701043.xml'}