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The Leibniz formula for divided difference operators associated to Kac-Moody root systems

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TitleInfo
Title
The Leibniz formula for divided difference operators associated to Kac-Moody root systems
Name (type = personal)
NamePart (type = family)
Samuel
NamePart (type = given)
Matthew Jason
NamePart (type = date)
1985-
DisplayForm
Matthew Samuel
Role
RoleTerm (authority = RULIB)
author
Name (type = personal)
NamePart (type = family)
Buch
NamePart (type = given)
Anders Skovsted
DisplayForm
Anders Skovsted Buch
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
chair
Name (type = personal)
NamePart (type = family)
Sahi
NamePart (type = given)
Siddhartha
DisplayForm
Siddhartha Sahi
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Advisory Committee
Role
RoleTerm (authority = RULIB)
internal member
Name (type = personal)
NamePart (type = family)
Retakh
NamePart (type = given)
Vladimir
DisplayForm
Vladimir Retakh
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
internal member
Name (type = personal)
NamePart (type = family)
Sottile
NamePart (type = given)
Frank
DisplayForm
Frank Sottile
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
outside member
Name (type = corporate)
NamePart
Rutgers University
Role
RoleTerm (authority = RULIB)
degree grantor
Name (type = corporate)
NamePart
Graduate School - New Brunswick
Role
RoleTerm (authority = RULIB)
school
TypeOfResource
Text
Genre (authority = marcgt)
theses
OriginInfo
DateCreated (qualifier = exact)
2014
DateOther (qualifier = exact); (type = degree)
2014-05
Place
PlaceTerm (type = code)
xx
Language
LanguageTerm (authority = ISO639-2b); (type = code)
eng
Abstract (type = abstract)
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)
NjNbRU
Genre (authority = ExL-Esploro)
ETD doctoral
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RightsDeclaration (ID = rulibRdec0006)
The author owns the copyright to this work.
RightsHolder (type = personal)
Name
FamilyName
Samuel
GivenName
Matthew
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime (encoding = w3cdtf); (qualifier = exact); (point = start)
2014-04-12 19:27:58
AssociatedEntity
Name
Matthew Samuel
Role
Copyright holder
Affiliation
Rutgers University. Graduate School - New Brunswick
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Type
License
Name
Author Agreement License
Detail
I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
Copyright
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Copyright protected
Availability
Status
Open
Reason
Permission or license
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RULTechMD (ID = TECHNICAL1)
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ETD
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windows xp
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