Arakawa-Suzuki functors for whittaker modules

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Title Arakawa-Suzuki functors for whittaker modules
Publication Type dissertation
School or College College of Science
Department Mathematics
Author Brown, Adam
Date 2019
Description In this dissertation, we construct a family of exact functors from the category of Whittaker modules of the simple complex Lie algebra of type An to the category of finite-dimensional modules of the graded affine Hecke algebra of type A`. Using results of Backelin and of Arakawa-Suzuki, we prove that these functors map standard modules to standard modules (or zero) and simple modules to simple modules (or zero). Moreover, we show that each simple module of the graded affine Hecke algebra appears as the image of a simple Whittaker module. Since the Whittaker category contains the BGG category O as a full subcategory, our results generalize results of Arakawa-Suzuki, which in turn generalize Schur-Weyl duality between finite-dimensional representations of SLn(C) and representations of the symmetric group Sn.
Type Text
Publisher University of Utah
Dissertation Name Doctor of Philosophy
Language eng
Rights Management (c) Adam Brown
Format application/pdf
Format Medium application/pdf
ARK ark:/87278/s6fz362q
Setname ir_etd
ID 1675806
Reference URL https://collections.lib.utah.edu/ark:/87278/s6fz362q
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