{"_id":"15339","date_updated":"2024-04-22T11:38:03Z","publication":"International Journal of Mathematics","article_type":"original","title":"Hitchin map on even very stable upward flows","author":[{"last_name":"González","full_name":"González, Miguel","first_name":"Miguel"},{"first_name":"Tamás","full_name":"Hausel, Tamás","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","last_name":"Hausel"}],"abstract":[{"text":"We define even very stable Higgs bundles and study the Hitchin map restricted to their upward flows. In the GLn case, we classify the type (1,…,1) examples, and find that they are governed by a root system formed by the roots of even height. We discuss how the spectrum of equivariant cohomology of real and quaternionic Grassmannians, 4n-spheres and the real Cayley plane appear to describe the Hitchin map on even cominuscule upward flows. The even upward flows in question are the same as upward flows in Higgs bundle moduli spaces for quasi-split inner real forms. The latter spaces have been pioneered by Oscar García-Prada and his collaborators.","lang":"eng"}],"year":"2024","publisher":"World Scientific Publishing","scopus_import":"1","day":"04","doi":"10.1142/S0129167X2441009X","publication_status":"epub_ahead","date_created":"2024-04-21T22:00:54Z","project":[{"grant_number":"P35847","name":"Geometry of the tip of the global nilpotent cone","_id":"34b2c9cb-11ca-11ed-8bc3-a50ba74ca4a3"}],"quality_controlled":"1","article_processing_charge":"No","month":"04","publication_identifier":{"eissn":["1793-6519"],"issn":["0129-167X"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"González, Miguel, and Tamás Hausel. “Hitchin Map on Even Very Stable Upward Flows.” <i>International Journal of Mathematics</i>, 2441009, World Scientific Publishing, 2024, doi:<a href=\"https://doi.org/10.1142/S0129167X2441009X\">10.1142/S0129167X2441009X</a>.","ama":"González M, Hausel T. Hitchin map on even very stable upward flows. <i>International Journal of Mathematics</i>. 2024. doi:<a href=\"https://doi.org/10.1142/S0129167X2441009X\">10.1142/S0129167X2441009X</a>","ista":"González M, Hausel T. 2024. Hitchin map on even very stable upward flows. International Journal of Mathematics., 2441009.","chicago":"González, Miguel, and Tamás Hausel. “Hitchin Map on Even Very Stable Upward Flows.” <i>International Journal of Mathematics</i>. World Scientific Publishing, 2024. <a href=\"https://doi.org/10.1142/S0129167X2441009X\">https://doi.org/10.1142/S0129167X2441009X</a>.","apa":"González, M., &#38; Hausel, T. (2024). Hitchin map on even very stable upward flows. <i>International Journal of Mathematics</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/S0129167X2441009X\">https://doi.org/10.1142/S0129167X2441009X</a>","ieee":"M. González and T. Hausel, “Hitchin map on even very stable upward flows,” <i>International Journal of Mathematics</i>. World Scientific Publishing, 2024.","short":"M. González, T. Hausel, International Journal of Mathematics (2024)."},"type":"journal_article","date_published":"2024-04-04T00:00:00Z","oa_version":"Preprint","external_id":{"arxiv":["2303.01404"]},"language":[{"iso":"eng"}],"status":"public","article_number":"2441009","oa":1,"acknowledgement":"Most of the research for this paper was done when the first author visited the second author's group at IST Austria as a summer intern in 2022. The second author was supported by an FWF grant \"Geometry of the top of the nilpotent cone\" number P35847.","department":[{"_id":"TaHa"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2303.01404"}]}