In this paper, we introduce a family of indecomposable finite-dimensional graded modules for the current algebra associated to a simple Lie algebra. These modules are indexed by an |R + |-tuple of partitions ξ = (ξ α ), where α varies over a set R + of positive roots of g and we assume that they satisfy a natural compatibility condition. In the case when the ξ α are all rectangular, for instance, we prove that these modules are Demazure modules in various levels. As a consequence we see that the defining relations of Demazure modules can be greatly simplified. We use this simplified presentation to relate our results to the fusion products, defined in [15], of representations of the current algebra. We prove that the Q-system of [22] extends to a canonical short exact sequence of fusion products of representations associated to certain special partitions ξ. Finally, in the last section we deal with the case of sl2 and prove that the modules we define are just fusion products of irreducible representations of the associated current algebra and give monomial bases for these modules.

Curating and analyzing centralized data repositories is a valuable approach in resolving the issue of reproducibility, gaining new insights and guiding future experiments, especially in the field of nanomaterials research. In this work, a data set containing processing information and mobility values of 115 DPP-DTT-based organic field effect transistors (OFET) was constructed from 15 publications. A customized classification algorithm was applied to the data set to help identify a reduced design region for polymer solution concentration that would be more likely to result in improved hole mobility. Experiments performed to confirm the insights from the data curation exercise revealed a strong influence of solution concentration on the polymer chain excitonic interactions and electronic performance. Devices fabricated at the critical chain overlap concentration of 5 g/L in chlorobenzene resulted in improved hole mobility, and were in good agreement with the insights provided by the classification algorithm.

Abstract. In this paper, we introduce a family of indecomposable finitedimensional graded modules for the twisted current algebras. These modules are indexed by an |R + |-tuple of partitions ξ = (ξ α ) α∈R + satisfying a natural compatibility condition. We give three equivalent presentations of these modules and show that for a particular choice of ξ these modules become isomorphic to Demazure modules in various levels for the twisted affine algebras. As a consequence we see that the defining relations of twisted Demazure modules can be greatly simplified. Furthermore, we investigate the notion of fusion products for twisted modules, first defined by Feigin and Loktev in 1999 for untwisted modules, and use the simplified presentation to prove a fusion product decomposition of twisted Demazure modules. As a consequence we prove that twisted Demazure modules can be obtained by taking the associated graded modules of (untwisted) Demazure modules for simply-laced affine algebras. Furthermore we give a semi-infinite fusion product construction for the irreducible representations of twisted affine algebras. Finally, we prove that the twisted Q-sytem defined by Hatayama et al. in 2001 extends to a non-canonical short exact sequence of fusion products of twisted Demazure modules.

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The advent of data analytics techniques and materials informatics provides opportunities to accelerate the discovery and development of organic semiconductors for electronic devices. However, the development of engineering solutions is limited by the ability to control thin-film morphology in an immense parameter space. The combination of highthroughput experimentation (HTE) laboratory techniques and data analytics offers tremendous avenues to traverse the expansive domains of tunable variables offered by organic semiconductor thin films. This Perspective outlines the steps required to incorporate a comprehensive informatics methodology into the experimental development of polymer-based organic semiconductor technologies. The translation of solution processing and property metrics to thin-film behavior is crucial to inform efficient HTE for data collection and application of data-centric tools to construct new process−structure−property relationships. We argue that detailed investigation of the solution state prior to deposition in conjunction with thin-film characterization will yield a deeper understanding of the physicochemical mechanisms influencing performance in π-conjugated polymer electronics, with data-driven approaches offering predictive capabilities previously unattainable via traditional experimental means.