Browsing by Author "Kujawa, Jonathan"

Now showing items 1-15 of 15

    • A-Species 

      Hausmann, Erin (2023-05-12)
      We introduce a generalized notion of combinatorial species called $A$-species, where $A$ is a Hopf algebra. The role played by the symmetric group, $S_n$, in the classical theory of species is now replaced with the wreath ...

    • Collective Behaviors of Quantum Emitters Coupled to a Structured Photonic Environment 

      Talukdar, Jugal (2023-07)
      The study of a quantum system coupled to an environment plays an indispensable role in expanding our understanding of quantum mechanics. It has a broad impact, encompassing fundamental inquiries in quantum physics as well ...

    • Complexity of Modules over Lie Superalgebras 

      El Turkey, Houssein (2014)
      In this dissertation, a fair amount of work is dedicated to computing the complexity of modules over a classical Lie superalgebra $\fg=\fg_{\0}\oplus \fg_{\1}$ over the complex numbers $\C$. We will consider the category ...

    • Dehn Functions of the Stallings-Bieri Groups and Constructions of Non-Unique Product Groups 

      Carter, William (2015-05-08)
      This thesis will consist of two separate halves in which we will present results concerning two different families of finitely generated torsion-free groups. The themes of each half are quite different and are related to ...

    • Diagrammatic Categories which arise from Directed Graphs 

      Reynolds, Ryan (2023-05-12)
      There is a categorical equivalence between the Temperley--Lieb category $TL(2)$ and the full subcategory of $SU(2)$-\textbf{mod} with objects given by $V^{\otimes k}$ where $V$ is the tautological $SU(2)$-module and $k$ ...

    • Generalized Polynomial Superfunctors 

      Randich, Joseph (2022-05-13)
      We introduce a generalized notion of homogeneous strict polynomial functors defined over a superalgebra, $A$. In particular, we define two closely related families of categories $\mathsf{P}^d_A$ and $\mathsf{P}^d_{(A,\ma ...

    • Investigating Abstract Algebra Students' Representational Fluency and Example-Based Intuitions 

      Lajos, Jessica (2021-08-05)
      The quotient group concept is a difficult for many students getting started in abstract algebra (Dubinsky et al., 1994; Melhuish, Lew, Hicks, and Kandasamy, 2020). The first study in this thesis explores an undergraduate, ...

    • K-types and Invariants for the Representations of GSp(4,R) 

      VerNooy, Colin (2019-08-01)
      Automorphic representations of the adelic group GSp (4 ,A Q ) are of importance in their relation to Siegel modular forms of degree 2. Given an automorphic representation π of GSp (4 ,A Q ), it decomposes into a product ...

    • On the Existence and Stability of Filiform Nilsolitons 

      Danser, Jordan (2022-08)
      This dissertation is concerned with the existence and stability of nilsoliton metrics on filiform Lie algebras. The results are presented in two major components. First, we give new results which preclude the existence of ...

    • On the Prescribed Ricci Curvature of Noncompact Homogeneous Spaces with Two Isotropy Summands 

      Gaskins, Dustin (2023-05-12)
      The current dissertation works within the setting of noncompact homogeneous spaces 𝐺/𝐻 in which 𝐺 is semi-simple. In particular, we frequently work with a decomposition of the Lie algebra 𝔤, 𝔤 = 𝔥 ⊕ 𝔭'' ⊕ 𝔭', ...

    • The representations of p-adic fields associated to elliptic curves 

      Turki, Salam (2015)
      The goal of this dissertation is to find the irreducible, admissible representation of GL(2; F) attached to an elliptic curve E over a p-adic field F. Associated to E is a 2-dimensional complex representation of the ...

    • Representations of the marked Brauer algebra 

      Tharp, Benjiman (2017-05-12)
      The marked Brauer algebra is a generalization of the diagrammatic Brauer algebra which diagrammatizes Moon's centralizer algebra for the type \mathfrak{p} Lie superalgebra. We prove that the marked Brauer algebra is a ...

    • Some Types And Covers For Quaternionic Hermitian Groups 

      Madsen, Thomas Laebel (2014-08-15)
      In this dissertation we determine the reducibility of certain induced representations. We do this using Bushnell and Kutzko's method of types and covers. We consider certain quaternionic hermitian groups over a $p$-adic ...

    • Two-boundary centralizer algebras for q(n) 

      Zhu, Jieru (2018-08)
      We define the degenerate two boundary affine Hecke-Clifford algebra $\mathcal{H}_d$, and show it admits a well-defined $\mathfrak{q}(n)$-linear action on the tensor space $M\otimes N\otimes V^{\otimes d}$, where $V$ is the ...

    • Webs for Type Q Lie Superalgebras 

      Brown, Gordon (2017-12-15)
      In the first part of this dissertation, we construct a monoidal supercategory whose morphism spaces are spanned by equivalence classes of diagrams called oriented type Q webs, modulo certain relations. We then prove a ...