Classical Invariants for Principal Series and Isomorphisms of Root Data

We develop some new techniques to calculate the Schur indicator for self-dual irreducible Langlands quotients of the principal series representations. Using these techniques we derive some new formulas for the Schur indicator and the real-quaternionic indicator. We make progress towards developing an algorithm to decide whether or not two root data are isomorphic. When the derived group has cyclic center, we solve the isomorphism problem completely. An immediate consequence is a clean and precise classification theorem for connected complex reductive groups whose derived groups have cyclic center.

School-Based Referrals to the Juvenile Courts: Prevalence and Characteristics in Several States

Effective school discipline practices are essential to keeping schools safe and creating an optimal learning environment. However, the overreliance of exclusionary discipline often removes students from the school setting and deprives them of the opportunity to learn. Previous research has suggested that students are being introduced to the juvenile justice system through the use of school-based juvenile court referrals. In 2011, approximately 1.2 million delinquency cases were referred to the juvenile courts in the United States. Preliminary evidence suggests that an increasing number of these referrals have originated in the schools. This study investigated school-based referrals to the juvenile courts as an element of the School-to-Prison Pipeline (StPP). The likelihood of school-based juvenile court referrals and rate of dismissal of these referrals was examined in several states using data from the National Juvenile Court Data Archives. In addition, the study examined race and special education status as predictors of school-based juvenile court referrals. Descriptive statistics, logistic regression and odds ratio, were used to analyze the data, make conclusions based on the findings and recommend appropriate school discipline practices.