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Spectral functions of invariant operators on skew multiplicity free spaces
Descriptive
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
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(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.
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electronic resource
Extent
vi, 84 p. : ill.
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Note
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Ph.D.
Note
Includes abstract
Note
Vita
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(type = bibliography)
Includes bibliographical references
Note
(type = statement of responsibility)
by Michael Weingart
Name
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Weingart
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Michael
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author
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Michael Weingart
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Knop
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Friedrich
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chair
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Friedrich Knop
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Goodman
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Roe
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Advisory Committee
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Roe Goodman
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NamePart
(type = family)
Sahi
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(type = given)
Siddhartha
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Advisory Committee
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Siddhartha Sahi
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(ID = NAME-5);
(type = personal)
NamePart
(type = family)
Nguyen
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(type = given)
Hieu
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outside member
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Advisory Committee
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Hieu Nguyen
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NamePart
Rutgers University
Role
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degree grantor
Name
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NamePart
Graduate School - New Brunswick
Role
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school
OriginInfo
DateCreated
(qualifier = exact)
2007
DateOther
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(type = degree)
2007
Place
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(type = code)
xx
RelatedItem
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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
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rucore19991600001
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NjNbRU
Identifier
(type = doi)
doi:10.7282/T3N016FP
Genre
(authority = ExL-Esploro)
ETD doctoral
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Rights
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The author owns the copyright to this work.
Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
RightsHolder
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(type = personal)
Name
FamilyName
Weingart
GivenName
Michael
Role
Copyright Holder
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(ID = RE-1);
(AUTHORITY = rulib)
Type
Permission or license
DateTime
2007-04-29 10:07:55
AssociatedEntity
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(AUTHORITY = rulib)
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Copyright holder
Name
Michael Weingart
Affiliation
Rutgers University. Graduate School - New Brunswick
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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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ETD
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399360
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