Diagrammatic Representation Theory of the Rank Two Symplectic Group

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dc.contributor.advisorElias, Ben
dc.contributor.authorBodish, Elijah
dc.date.accessioned2022-10-04T19:32:51Z
dc.date.available2022-10-04T19:32:51Z
dc.date.issued2022-10-04
dc.description.abstractWe study the diagrammatic representation theory of the group $Sp_4$ and the quantum group $U_q(\mathfrak{sp}_4)$, expanding on the previous results of Kuperberg about type $B_2= C_2$ webs. In particular, we construct a basis for an integral form of Kuperberg's web category. Using this basis we prove that the Karoubi envelope of the $C_2$ web category is equivalent to the category of tilting modules $\Tilt(U_q(\mathfrak{sp}_4))$. We also use the basis to give recursive formulas for the idempotent projecting to a top summand in a tensor product of fundamental representations. Finally, using our result about the equivalence between Kuperberg's web category and $\Tilt(U_q(\mathfrak{sp}_4))$, we prove that when $[3]=0$ or $[4] = 0$, the semisimple quotient of $U_q(\mathfrak{sp}_4)$ is equivalent to $\Rep(O(2))$. This dissertation contains previously published material.en_US
dc.identifier.urihttps://hdl.handle.net/1794/27571
dc.language.isoen_US
dc.publisherUniversity of Oregon
dc.rightsAll Rights Reserved.
dc.subjectclaspen_US
dc.subjectJones-Wenzl idempotenten_US
dc.subjectrepresentation theoryen_US
dc.subjectspideren_US
dc.subjecttilting modulesen_US
dc.subjectwebsen_US
dc.titleDiagrammatic Representation Theory of the Rank Two Symplectic Group
dc.typeElectronic Thesis or Dissertation
thesis.degree.disciplineDepartment of Mathematics
thesis.degree.grantorUniversity of Oregon
thesis.degree.leveldoctoral
thesis.degree.namePh.D.

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