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Spectral functions of invariant operators on skew multiplicity free spaces

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TypeOfResource
Text
TitleInfo (ID = T-1)
Title
Spectral functions of invariant operators on skew multiplicity free spaces
Identifier
ETD_205
Identifier (type = hdl)
http://hdl.rutgers.edu/1782.1/rucore10001600001.ETD.000054799
Language
LanguageTerm (authority = ISO639-2); (type = code)
eng
Genre (authority = marcgt)
theses
Subject (ID = SBJ-1); (authority = RUETD)
Topic
Mathematics
Subject (ID = SBJ-2); (authority = ETD-LCSH)
Topic
Differential operators
Subject (ID = SBJ-3); (authority = ETD-LCSH)
Topic
Skew fields
Subject (ID = SBJ-4); (authority = ETD-LCSH)
Topic
Combinatorial analysis
Abstract (type = abstract)
This thesis extends results on spectral functions of invariant differential operators on multiplicity free spaces to the setting of skew multiplicity free spaces, which are representations of a reductive group whose exterior algebra decomposes into a direct sum of pairwise nonisomorphic irreducibles. We prove in the general skew multiplicity free case that the spectral functions satisfy a vanishing property and a transposition formula which are formally identical to those satisfied by their multiplicity free analogues. We investigate two special cases, the GL_nC modules S^2C^n and Wedge^2 C^n, for which the spectral functions of invariant operators form a family of supersymmetric functions which can be identified with the factorial Schur Q functions. From this equivalence we deduce several properties of each family, giving the spectral functions a combinatorial interpretation and the factorial Schur Q functions a new representation theoretic one.
PhysicalDescription
Form (authority = gmd)
electronic resource
Extent
vi, 84 p. : ill.
InternetMediaType
application/pdf
InternetMediaType
text/xml
Note (type = degree)
Ph.D.
Note
Includes abstract
Note
Vita
Note (type = bibliography)
Includes bibliographical references
Note (type = statement of responsibility)
by Michael Weingart
Name (ID = NAME-1); (type = personal)
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Weingart
NamePart (type = given)
Michael
Role
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author
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Michael Weingart
Name (ID = NAME-2); (type = personal)
NamePart (type = family)
Knop
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Friedrich
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chair
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Advisory Committee
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Friedrich Knop
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NamePart (type = family)
Goodman
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Roe
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internal member
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Advisory Committee
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Roe Goodman
Name (ID = NAME-4); (type = personal)
NamePart (type = family)
Sahi
NamePart (type = given)
Siddhartha
Role
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internal member
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Advisory Committee
DisplayForm
Siddhartha Sahi
Name (ID = NAME-5); (type = personal)
NamePart (type = family)
Nguyen
NamePart (type = given)
Hieu
Role
RoleTerm (authority = RULIB)
outside member
Affiliation
Advisory Committee
DisplayForm
Hieu Nguyen
Name (ID = NAME-1); (type = corporate)
NamePart
Rutgers University
Role
RoleTerm (authority = RULIB)
degree grantor
Name (ID = NAME-2); (type = corporate)
NamePart
Graduate School - New Brunswick
Role
RoleTerm (authority = RULIB)
school
OriginInfo
DateCreated (qualifier = exact)
2007
DateOther (qualifier = exact); (type = degree)
2007
Place
PlaceTerm (type = code)
xx
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
Location
PhysicalLocation (authority = marcorg); (displayLabel = Rutgers, The State University of New Jersey)
NjNbRU
Identifier (type = doi)
doi:10.7282/T3N016FP
Genre (authority = ExL-Esploro)
ETD doctoral
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Rights

RightsDeclaration (AUTHORITY = GS); (ID = rulibRdec0006)
The author owns the copyright to this work.
Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
RightsHolder (ID = PRH-1); (type = personal)
Name
FamilyName
Weingart
GivenName
Michael
Role
Copyright Holder
RightsEvent (ID = RE-1); (AUTHORITY = rulib)
Type
Permission or license
DateTime
2007-04-29 10:07:55
AssociatedEntity (ID = AE-1); (AUTHORITY = rulib)
Role
Copyright holder
Name
Michael Weingart
Affiliation
Rutgers University. Graduate School - New Brunswick
AssociatedObject (ID = AO-1); (AUTHORITY = rulib)
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.
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Technical

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ETD
MimeType (TYPE = file)
application/pdf
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application/x-tar
FileSize (UNIT = bytes)
399360
Checksum (METHOD = SHA1)
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