{"author":[{"first_name":"Fabian","last_name":"Januszewski","full_name":"Januszewski, Fabian"}],"citation":{"apa":"Januszewski, F. (2021). Towards a tensor-classification of Harish-Chandra modules: The case  SL_2(R). In <i>arXiv:2104.01475</i>.","chicago":"Januszewski, Fabian. “Towards a Tensor-Classification of Harish-Chandra Modules: The Case  SL_2(R).” <i>ArXiv:2104.01475</i>, 2021.","bibtex":"@article{Januszewski_2021, title={Towards a tensor-classification of Harish-Chandra modules: The case  SL_2(R)}, journal={arXiv:2104.01475}, author={Januszewski, Fabian}, year={2021} }","short":"F. Januszewski, ArXiv:2104.01475 (2021).","mla":"Januszewski, Fabian. “Towards a Tensor-Classification of Harish-Chandra Modules: The Case  SL_2(R).” <i>ArXiv:2104.01475</i>, 2021.","ama":"Januszewski F. Towards a tensor-classification of Harish-Chandra modules: The case  SL_2(R). <i>arXiv:210401475</i>. Published online 2021.","ieee":"F. Januszewski, “Towards a tensor-classification of Harish-Chandra modules: The case  SL_2(R),” <i>arXiv:2104.01475</i>. 2021."},"status":"public","date_created":"2025-03-28T08:43:39Z","user_id":"81636","language":[{"iso":"eng"}],"abstract":[{"text":"We consider the category of Harish-Chandra modules for ${\\rm SL}_2(\\mathbb\r\nR)$ as a module over the category of finite-dimensional representations of\r\n${\\rm SL}(2)$ with respect to the tensor product. In this note we use classical\r\nresults about principal series to obtain a classification of\r\n$\\otimes$-submodules of the category of Harish-Chandra modules of ${\\rm\r\nSL}_2(\\mathbb R)$. The resulting classification recovers the classical\r\nclassification of irreducible Harish-Chandra modules. Our methods are expected\r\nto generalize to arbitrary reductive pairs and more general base fields.","lang":"eng"}],"year":"2021","date_updated":"2025-03-28T08:44:56Z","_id":"59181","publication":"arXiv:2104.01475","external_id":{"arxiv":["2104.01475"]},"type":"preprint","title":"Towards a tensor-classification of Harish-Chandra modules: The case  SL_2(R)"}