[{"_id":"66293","language":[{"iso":"eng"}],"user_id":"72064","author":[{"id":"72064","last_name":"Burban","first_name":"Igor","full_name":"Burban, Igor"},{"last_name":"Gnedin","first_name":"Wassilij","full_name":"Gnedin, Wassilij"}],"status":"public","year":"2026","title":"Representation theory of the Gelfand quiver and Harish-Chandra modules for SL_2(R)","date_updated":"2026-07-07T06:29:40Z","date_created":"2026-07-07T06:28:32Z","external_id":{"arxiv":["2604.00274"]},"type":"preprint","citation":{"ama":"Burban I, Gnedin W. Representation theory of the Gelfand quiver and Harish-Chandra modules for SL_2(R). <i>arXiv:260400274</i>. Published online 2026.","bibtex":"@article{Burban_Gnedin_2026, title={Representation theory of the Gelfand quiver and Harish-Chandra modules for SL_2(R)}, journal={arXiv:2604.00274}, author={Burban, Igor and Gnedin, Wassilij}, year={2026} }","mla":"Burban, Igor, and Wassilij Gnedin. “Representation Theory of the Gelfand Quiver and Harish-Chandra Modules for SL_2(R).” <i>ArXiv:2604.00274</i>, 2026.","chicago":"Burban, Igor, and Wassilij Gnedin. “Representation Theory of the Gelfand Quiver and Harish-Chandra Modules for SL_2(R).” <i>ArXiv:2604.00274</i>, 2026.","short":"I. Burban, W. Gnedin, ArXiv:2604.00274 (2026).","apa":"Burban, I., &#38; Gnedin, W. (2026). Representation theory of the Gelfand quiver and Harish-Chandra modules for SL_2(R). In <i>arXiv:2604.00274</i>.","ieee":"I. Burban and W. Gnedin, “Representation theory of the Gelfand quiver and Harish-Chandra modules for SL_2(R),” <i>arXiv:2604.00274</i>. 2026."},"publication":"arXiv:2604.00274","abstract":[{"lang":"eng","text":"In 1970, Gelfand posed the problem of classifying the indecomposable objects in a representation category equivalent to the principal block of Harish-Chandra modules for $\\mathsf{SL}_2(\\mathbb{R})$; explicit solutions were obtained by Bondarenko, and, independently, Crawley-Boevey. In this article, we give a complete answer to Gelfand's problem from a derived category perspective. We classify indecomposable objects in the bounded derived category of nilpotent representations of the Gelfand quiver in terms of band and string complexes, and determine their images under the derived Auslander-Reiten translation, the sign involution, and the contragredient duality. The four main combinatorial classes are characterized in Lie-theoretic as well as homological terms. For the abelian category of nilpotent representations, we provide projective resolutions, standard homological invariants and explicit representation matrices of all indecomposables. Our approach can be extended to arrow ideal completions of path algebras of skew-gentle quivers."}]},{"title":"Representation theory of the real Gelfand order and real Harish-Chandra modules for SL_2(R)","year":"2026","status":"public","author":[{"last_name":"Burban","first_name":"Igor","full_name":"Burban, Igor","id":"72064"},{"full_name":"Drozd, Yuriy","first_name":"Yuriy","last_name":"Drozd"}],"date_updated":"2026-07-07T06:23:43Z","_id":"66292","language":[{"iso":"eng"}],"user_id":"72064","publication":"arXiv:2605.18000","citation":{"mla":"Burban, Igor, and Yuriy Drozd. “Representation Theory of the Real Gelfand Order and Real Harish-Chandra Modules for SL_2(R).” <i>ArXiv:2605.18000</i>, 2026.","bibtex":"@article{Burban_Drozd_2026, title={Representation theory of the real Gelfand order and real Harish-Chandra modules for SL_2(R)}, journal={arXiv:2605.18000}, author={Burban, Igor and Drozd, Yuriy}, year={2026} }","ama":"Burban I, Drozd Y. Representation theory of the real Gelfand order and real Harish-Chandra modules for SL_2(R). <i>arXiv:260518000</i>. Published online 2026.","ieee":"I. Burban and Y. Drozd, “Representation theory of the real Gelfand order and real Harish-Chandra modules for SL_2(R),” <i>arXiv:2605.18000</i>. 2026.","apa":"Burban, I., &#38; Drozd, Y. (2026). Representation theory of the real Gelfand order and real Harish-Chandra modules for SL_2(R). In <i>arXiv:2605.18000</i>.","chicago":"Burban, Igor, and Yuriy Drozd. “Representation Theory of the Real Gelfand Order and Real Harish-Chandra Modules for SL_2(R).” <i>ArXiv:2605.18000</i>, 2026.","short":"I. Burban, Y. Drozd, ArXiv:2605.18000 (2026)."},"abstract":[{"lang":"eng","text":"In this article we study the principal block of the category of real Harish-Chandra modules for the group $\\mathsf{SL}_2(\\RR)$ and relate it to the category of finite dimensional modules over the so-called real Gelfand order. We describe several distinguished classes of the corresponding indecomposable representations."}],"external_id":{"arxiv":["2605.18000"]},"date_created":"2026-07-07T06:22:32Z","type":"preprint"},{"user_id":"103440","_id":"63620","language":[{"iso":"eng"}],"date_updated":"2026-07-06T07:56:11Z","author":[{"first_name":"Barbara","last_name":"Baumeister","full_name":"Baumeister, Barbara"},{"id":"72064","full_name":"Burban, Igor","first_name":"Igor","last_name":"Burban"},{"full_name":"Neaime, Georges","last_name":"Neaime","first_name":"Georges"},{"full_name":"Schwabe, Charly Merlin","first_name":"Charly Merlin","last_name":"Schwabe","id":"103440"}],"title":"Non-crossing partitions for exceptional hereditary curves","status":"public","year":"2025","type":"preprint","date_created":"2026-01-15T09:37:34Z","external_id":{"arxiv":["2512.01729"]},"abstract":[{"text":"We introduce a new class of reflection groups associated with the canonical bilinear lattices of Lenzing, which we call reflection groups of canonical type. The main result of this work is a categorification of the corresponding poset of non-crossing partitions for any such group, realized via the poset of thick subcategories of the category of coherent sheaves on an exceptional hereditary curve generated by an exceptional sequence. A second principal result, essential for the categorification, is a proof of the transitivity of the Hurwitz action in these reflection groups.","lang":"eng"}],"citation":{"bibtex":"@article{Baumeister_Burban_Neaime_Schwabe_2025, title={Non-crossing partitions for exceptional hereditary curves}, journal={arXiv:2512.01729}, author={Baumeister, Barbara and Burban, Igor and Neaime, Georges and Schwabe, Charly Merlin}, year={2025} }","ama":"Baumeister B, Burban I, Neaime G, Schwabe CM. Non-crossing partitions for exceptional hereditary curves. <i>arXiv:251201729</i>. Published online 2025.","mla":"Baumeister, Barbara, et al. “Non-Crossing Partitions for Exceptional Hereditary Curves.” <i>ArXiv:2512.01729</i>, 2025.","chicago":"Baumeister, Barbara, Igor Burban, Georges Neaime, and Charly Merlin Schwabe. “Non-Crossing Partitions for Exceptional Hereditary Curves.” <i>ArXiv:2512.01729</i>, 2025.","short":"B. Baumeister, I. Burban, G. Neaime, C.M. Schwabe, ArXiv:2512.01729 (2025).","ieee":"B. Baumeister, I. Burban, G. Neaime, and C. M. Schwabe, “Non-crossing partitions for exceptional hereditary curves,” <i>arXiv:2512.01729</i>. 2025.","apa":"Baumeister, B., Burban, I., Neaime, G., &#38; Schwabe, C. M. (2025). Non-crossing partitions for exceptional hereditary curves. In <i>arXiv:2512.01729</i>."},"publication":"arXiv:2512.01729"},{"abstract":[{"lang":"eng","text":"In this paper, we study properties of nodal orders defined over arbitrary base fields. In particular we give a classification of complete real nodal orders."}],"publication":"arXiv:2410.05792","citation":{"chicago":"Burban, Igor, and Yuriy Drozd. “Classification of Real Nodal Orders.” <i>ArXiv:2410.05792</i>, 2024.","short":"I. Burban, Y. Drozd, ArXiv:2410.05792 (2024).","ieee":"I. Burban and Y. Drozd, “Classification of real nodal orders,” <i>arXiv:2410.05792</i>. 2024.","apa":"Burban, I., &#38; Drozd, Y. (2024). Classification of real nodal orders. In <i>arXiv:2410.05792</i>.","bibtex":"@article{Burban_Drozd_2024, title={Classification of real nodal orders}, journal={arXiv:2410.05792}, author={Burban, Igor and Drozd, Yuriy}, year={2024} }","ama":"Burban I, Drozd Y. Classification of real nodal orders. <i>arXiv:241005792</i>. Published online 2024.","mla":"Burban, Igor, and Yuriy Drozd. “Classification of Real Nodal Orders.” <i>ArXiv:2410.05792</i>, 2024."},"type":"preprint","external_id":{"arxiv":["2410.05792"]},"date_created":"2026-07-07T06:32:11Z","date_updated":"2026-07-07T06:32:30Z","status":"public","title":"Classification of real nodal orders","year":"2024","author":[{"full_name":"Burban, Igor","last_name":"Burban","first_name":"Igor","id":"72064"},{"first_name":"Yuriy","last_name":"Drozd","full_name":"Drozd, Yuriy"}],"user_id":"72064","_id":"66295","language":[{"iso":"eng"}]},{"citation":{"mla":"Burban, Igor, et al. <i>A Classification of Polyharmonic Maaß Forms via Quiver Representations</i>. 2022.","ama":"Burban I, Alfes-Neumann C, Raum M. A classification of polyharmonic Maaß forms via quiver representations. Published online 2022.","bibtex":"@article{Burban_Alfes-Neumann_Raum_2022, title={A classification of polyharmonic Maaß forms via quiver representations}, author={Burban, Igor and Alfes-Neumann, C. and Raum, M.}, year={2022} }","apa":"Burban, I., Alfes-Neumann, C., &#38; Raum, M. (2022). <i>A classification of polyharmonic Maaß forms via quiver representations</i>.","ieee":"I. Burban, C. Alfes-Neumann, and M. Raum, “A classification of polyharmonic Maaß forms via quiver representations.” 2022.","short":"I. Burban, C. Alfes-Neumann, M. Raum, (2022).","chicago":"Burban, Igor, C. Alfes-Neumann, and M. Raum. “A Classification of Polyharmonic Maaß Forms via Quiver Representations,” 2022."},"type":"preprint","department":[{"_id":"602"}],"date_created":"2023-05-07T00:54:50Z","publication_status":"published","date_updated":"2026-07-07T06:20:58Z","status":"public","year":"2022","title":"A classification of polyharmonic Maaß forms via quiver representations","author":[{"id":"72064","last_name":"Burban","first_name":"Igor","full_name":"Burban, Igor"},{"full_name":"Alfes-Neumann, C.","last_name":"Alfes-Neumann","first_name":"C."},{"full_name":"Raum, M.","first_name":"M.","last_name":"Raum"}],"user_id":"72064","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2207.02278"}],"language":[{"iso":"eng"}],"_id":"44537"},{"user_id":"49063","language":[{"iso":"eng"}],"_id":"44538","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1805.05174"}],"publication_status":"published","date_updated":"2023-05-07T01:36:42Z","author":[{"last_name":"Burban","first_name":"Igor","full_name":"Burban, Igor","id":"72064"},{"full_name":"Drozd, Yu.","first_name":"Yu.","last_name":"Drozd"}],"status":"public","title":"Non-commutative nodal curves and derived tame algebras","year":"2018","department":[{"_id":"602"}],"type":"preprint","date_created":"2023-05-07T00:56:31Z","citation":{"ieee":"I. Burban and Yu. Drozd, “Non-commutative nodal curves and derived tame algebras.” 2018.","apa":"Burban, I., &#38; Drozd, Yu. (2018). <i>Non-commutative nodal curves and derived tame algebras</i>.","chicago":"Burban, Igor, and Yu. Drozd. “Non-Commutative Nodal Curves and Derived Tame Algebras,” 2018.","short":"I. Burban, Yu. Drozd, (2018).","mla":"Burban, Igor, and Yu. Drozd. <i>Non-Commutative Nodal Curves and Derived Tame Algebras</i>. 2018.","bibtex":"@article{Burban_Drozd_2018, title={Non-commutative nodal curves and derived tame algebras}, author={Burban, Igor and Drozd, Yu.}, year={2018} }","ama":"Burban I, Drozd Yu. Non-commutative nodal curves and derived tame algebras. Published online 2018."}},{"type":"preprint","department":[{"_id":"602"}],"date_created":"2023-05-07T00:57:34Z","extern":"1","citation":{"bibtex":"@article{Burban_Drozd_2017, title={On the derived categories of gentle and skew-gentle algebras: homological algebra and matrix problems}, author={Burban, Igor and Drozd, Yu.}, year={2017} }","ama":"Burban I, Drozd Yu. On the derived categories of gentle and skew-gentle algebras: homological algebra and matrix problems. Published online 2017.","mla":"Burban, Igor, and Yu. Drozd. <i>On the Derived Categories of Gentle and Skew-Gentle Algebras: Homological Algebra and Matrix Problems</i>. 2017.","chicago":"Burban, Igor, and Yu. Drozd. “On the Derived Categories of Gentle and Skew-Gentle Algebras: Homological Algebra and Matrix Problems,” 2017.","short":"I. Burban, Yu. Drozd, (2017).","ieee":"I. Burban and Yu. Drozd, “On the derived categories of gentle and skew-gentle algebras: homological algebra and matrix problems.” 2017.","apa":"Burban, I., &#38; Drozd, Yu. (2017). <i>On the derived categories of gentle and skew-gentle algebras: homological algebra and matrix problems</i>."},"user_id":"49063","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1706.08358"}],"language":[{"iso":"eng"}],"_id":"44539","date_updated":"2023-05-07T01:36:54Z","publication_status":"published","year":"2017","title":"On the derived categories of gentle and skew-gentle algebras: homological algebra and matrix problems","status":"public","author":[{"last_name":"Burban","first_name":"Igor","full_name":"Burban, Igor","id":"72064"},{"first_name":"Yu.","last_name":"Drozd","full_name":"Drozd, Yu."}]}]