The Real-Quaternionic Indicator of Irreducible Self-Conjugate Representations of Real Reductive Algebraic Groups and A Comment on the Local Langlands Correspondence of GL(2, F )

The real-quaternionic indicator, also called the $\delta$ indicator, indicates if a self-conjugate representation is of real or quaternionic type. It is closely related to the Frobenius-Schur indicator, which we call the $\varepsilon$ indicator. The Frobenius-Schur indicator $\varepsilon(\pi)$ is known to be given by a particular value of the central character. We would like a similar result for the $\delta$ indicator. When $G$ is compact, $\delta(\pi)$ and $\varepsilon(\pi)$ coincide. In general, they are not necessarily the same. In this thesis, we will give a relation between the two indicators when $G$ is a real reductive algebraic group. This relation also leads to a formula for $\delta(\pi)$ in terms of the central character. For the second part, we consider the construction of the local Langlands correspondence of $GL(2,F)$ when $F$ is a non-Archimedean local field with odd residual characteristics. By re-examining the construction, we provide new proofs to some important properties of the correspondence. Namely, the construction is independent of the choice of additive character in the theta correspondence.

Water Quality Impacts due to the Addition of Biosolids-Derived Compost to Bioretention

Bioretention is a common stormwater control measure (SCM). While compost, combined with other bioretention soil media (BSM), has the potential for increased pollutant and water uptake and storage, it also may leach harmful nutrients. Limited information is available on the use of compost in SCMs. Therefore, this project seeks to analyze the impacts of the addition of biosolids-derived compost to bioretention. To accomplish this, bioretention mesocosm column studies were conducted to determine the leaching effects of 15%, 30%, and 30% tap water-washed compost, mixed with standard BSM. Synthetic storm runoff was applied to the columns and the effluent was analyzed for total nitrogen (N), phosphorus (P), and their speciation. All three columns leached N and P with maximum total N concentrations of 2,200, 2,100, and 300 mg-N/L and total P concentrations of 12, 4.9, and 4.6 mg-P/L for the 30%, 15%, and 30% washed mesocosms, respectively. Therefore, based on this study, it is not recommended that biosolids-derived compost be added to bioretention media.