In this dissertation we present a new Leibniz formula (i.e. generalized product rule) for the type of divided difference operators first introduced by Bernšteĭn, Gel'fand, and Gel'fand. The formula applies for divided difference operators associated to the geometric representation of the Coxeter system of any Kac-Moody group, be it finite-dimensional or infinite-dimensional. Our formula shows that in order to study the structure of the equivariant cohomology ring there is no need to actually construct it at all because the structure constants are encoded in our Leibniz formula for divided difference operators. The formula may be used to compute the structure constants and prove general results about them. In the future our results may be useful in finding Littlewood-Richardson rules in equivariant cohomology and may make the study of certain problems in Schubert calculus more accessible to researchers who are not necessarily well-versed in algebro-geometric or topological methods.
Subject (authority = RUETD)
Topic
Mathematics
Subject (authority = ETD-LCSH)
Topic
Root systems (Algebra)
Subject (authority = ETD-LCSH)
Topic
Difference operators
RelatedItem (type = host)
TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
RelatedItem (type = host)
TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier (type = local)
rucore19991600001
Identifier
ETD_5470
Identifier (type = doi)
doi:10.7282/T3NG4NZR
PhysicalDescription
Form (authority = gmd)
electronic resource
InternetMediaType
application/pdf
InternetMediaType
text/xml
Extent
v, 34 p. : ill.
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references
Note (type = statement of responsibility)
by Matthew Jason Samuel
Location
PhysicalLocation (authority = marcorg); (displayLabel = Rutgers, The State University of New Jersey)
Rutgers University. Graduate School - New Brunswick
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Type
License
Name
Author Agreement License
Detail
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