Spherical Elements in the Affine Yokonuma-Hecke Algebra

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dc.contributor.authorShaplin, Richard Martin IIIen
dc.contributor.committeechairOrr, Daniel D.en
dc.contributor.committeememberLinnell, Peter A.en
dc.contributor.committeememberShimozono, Mark M.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2020-07-09T08:01:11Zen
dc.date.available2020-07-09T08:01:11Zen
dc.date.issued2020-07-08en
dc.description.abstractIn Chapter 1 we introduce the Yokonuma-Hecke Algebra and a Yokonuma-Hecke Algebra-module. In Chapter 2 we determine that the possible eigenvalues of particular elements in the Yokonuma-Hecke Algebra acting on the module. In Chapter 3 we find determine module subspaces and eigenspaces that are isomorphic. In Chapter 4 we determine the structure of the q-eigenspace. In Chapter 5 we determine the spherical elements of the module.en
dc.description.abstractgeneralThe Yokonuma-Hecke Algebra-module is a vector space over a particular field. Acting on vectors from the module by any element of the Yokonuma-Hecke Algebra corresponds to a linear transformation. Then, for each element we can find eigenvalues and eigenvectors. The transformations that we are considering all have the same eigenvalues. So, we consider the intersection of all the eigenspaces that correspond to the same eigenvalue. I.e. vectors that are eigenvectors of all of the elements. We find an algorithm that generates a basis for said vectors.en
dc.description.degreeMaster of Scienceen
dc.format.mediumETDen
dc.identifier.othervt_gsexam:26025en
dc.identifier.urihttp://hdl.handle.net/10919/99307en
dc.publisherVirginia Techen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectAffine Yokonuma–Hecke Algebrasen
dc.subjectSpherical Elementsen
dc.titleSpherical Elements in the Affine Yokonuma-Hecke Algebraen
dc.typeThesisen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.levelmastersen
thesis.degree.nameMaster of Scienceen

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