Irreducible representations of the rational Cherednik algebra associated to the Coxeter group H_3

This paper describes irreducible representations in category O of the rational Cherednik algebra H_c(H_3,h) associated to the exceptional Coxeter group H_3 and any complex parameter c. We compute the characters of all these representations explicitly. As a consequence, we classify all the finite dimensional irreducible representations of H_c(H_3,h).Comment: Version 2: a minor error in 5.1 and its consequences in 3.1. and 3.2 corrected. Comments welcom

Mapping each pre-existing condition’s association to short-term and long-term COVID-19 complications

Abstract Understanding the relationships between pre-existing conditions and complications of COVID-19 infection is critical to identifying which patients will develop severe disease. Here, we leverage ~1.1 million clinical notes from 1803 hospitalized COVID-19 patients and deep neural network models to characterize associations between 21 pre-existing conditions and the development of 20 complications (e.g. respiratory, cardiovascular, renal, and hematologic) of COVID-19 infection throughout the course of infection (i.e. 0–30 days, 31–60 days, and 61–90 days). Pleural effusion was the most frequent complication of early COVID-19 infection (89/1803 patients, 4.9%) followed by cardiac arrhythmia (45/1803 patients, 2.5%). Notably, hypertension was the most significant risk factor associated with 10 different complications including acute respiratory distress syndrome, cardiac arrhythmia, and anemia. The onset of new complications after 30 days is rare and most commonly involves pleural effusion (31–60 days: 11 patients, 61–90 days: 9 patients). Lastly, comparing the rates of complications with a propensity-matched COVID-negative hospitalized population confirmed the importance of hypertension as a risk factor for early-onset complications. Overall, the associations between pre-COVID conditions and COVID-associated complications presented here may form the basis for the development of risk assessment scores to guide clinical care pathways