Hassett, Brendan E.2014-10-172014-10-172014-052014-04-22May 2014Zhang, Letao. "Deformations of Hilbert Schemes of Points on K3 Surfaces and Representation Theory." (2014) Diss., Rice University. <a href="https://hdl.handle.net/1911/77609">https://hdl.handle.net/1911/77609</a>.https://hdl.handle.net/1911/77609We study the cohomology rings of Kaehler deformations X of Hilbert schemes of points on K3 surfaces by representation theory. We compute the graded character formula of the Mumford - Tate group representation on the cohomology ring of X. Furthermore, we also study the Hodge structure of X, and find the generating series for deducting the number of canaonical Hodge classes in the middle cohomology.application/pdfengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.Hilbert schemeRepresentation theoryHyperkaehler manifoldsThesis2014-10-17