2026-09-23T16:15:53Zhttps://ubir.buffalo.edu/oai/request

oai:ubir.buffalo.edu:10477/781212025-09-18T03:15:21Zcom_10477_77914col_10477_77915

On the Induced Module of the symmetric group from the Gelfand-Zetlin subalgebra Su, Yin Hemmer, David Mathematics mathematics Ph.D. In my dissertation, the induced modules $\Ind[\alpha]$ are studied. For a weight $[\alpha]\in \F^n$, $\Ind[\alpha]$ is defined to be an $\F\S_n$-module, that is induced from a module $I[\alpha]$, over the Gelfand-Zetlin subalgebra, generated by the Murphy's elements. In this paper, an epimorphism the induced module to the dual Specht module is defined over fields of any characteristic. In characteristic $0$, it will be shown that each nonzero induced module $\Ind[\alpha]$ is isomorphic to a Specht module. In characteristic p, I will discuss when the induced module is nonzero, and show that all composition factors belong to a single block of $\F\S_n$. 2018-06-28T20:34:22Z 2018-06-28T20:34:22Z 2018 2018-05-18 11:35:28 Text Dissertation http://hdl.handle.net/10477/78121 eng Users of works found in University at Buffalo Institutional Repository (UBIR) are responsible for identifying and contacting the copyright owner for permission to reuse. University at Buffalo Libraries do not manage rights for copyright-protected works and cannot assist with permissions. Copyright retained by author. application/pdf State University of New York at Buffalo