Electronic Theses and Dissertations

# Coefficient Space Properties and a Schur Algebra Generalization

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dc.contributor.authorTurner, Daviden_US
dc.date.accessioned2008-09-09T21:18:24Z
dc.date.available2008-09-09T21:18:24Z
dc.date.issued2005-12-15en_US
dc.identifier.urihttp://hdl.handle.net/10415/479
dc.description.abstractLet K be an infinite field and Gamma = GL_(n)(K). If we linearly extend the natural action of Gamma on the set E of n-dimensional column vectors over K to the group algebra KGamma, then E becomes a KGamma-module. We then construct the KGamma-module E^(otimes r), the r-fold tensor product of E. The image S_(r)(Gamma) of the corresponding representation of KGamma is called the Schur algebra. If E is replaced by a different KGamma-module L, the same construction results in an algebra S_(r,\,L). The subalgebra A(n) of K^(Gamma) generated by the coordinate functions c_(alpha beta) from Gamma to K with 1 <= alpha, beta <= n is a bialgebra. A(n) has a subcoalgebra A_(r) which consists of homogeneous polynomials of total degree r in the indeterminants c_(alpha beta). Classically, the dual A_(r)^* of A_(r) is an algebra isomorphic to S_(r)(Gamma) and A_(r) is the coefficient space of E^(otimes r). We identify S_(r, L) with the dual A_(r, L)^* of the coefficient space A_(r, L) of L^(otimes r) and give a description of A_(r, L).en_US
dc.language.isoen_USen_US
dc.subjectMathematics and Statisticsen_US
dc.titleCoefficient Space Properties and a Schur Algebra Generalizationen_US
dc.typeDissertationen_US
dc.embargo.lengthNO_RESTRICTIONen_US
dc.embargo.statusNOT_EMBARGOEDen_US