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dc.contributor.authorTaylor, Jay
dc.date.accessioned2019-04-25T22:48:06Z
dc.date.available2019-04-25T22:48:06Z
dc.date.issued2019-05
dc.identifier.citationThe Structure of Root Data and Smooth Regular Embeddings of Reductive Groups, Proc. Edinb. Math. Soc. (2) 62 (2019), no. 2, 523-552.en_US
dc.identifier.issn0013-0915
dc.identifier.doi10.1017/S0013091518000597
dc.identifier.urihttp://hdl.handle.net/10150/632109
dc.description.abstractWe investigate the structure of root data by considering their decomposition as a product of a semisimple root datum and a torus. Using this decomposition, we obtain a parametrization of the isomorphism classes of all root data. By working at the level of root data, we introduce the notion of a smooth regular embedding of a connected reductive algebraic group, which is a refinement of the commonly used regular embeddings introduced by Lusztig. In the absence of Steinberg endomorphisms, such embeddings were constructed by Benjamin Martin. In an unpublished manuscript, Asai proved three key reduction techniques that are used for reducing statements about arbitrary connected reductive algebraic groups, equipped with a Frobenius endomorphism, to those whose derived subgroup is simple and simply connected. Using our investigations into root data we give new proofs of Asai's results and generalize them so that they are compatible with Steinberg endomorphisms. As an illustration of these ideas, we answer a question posed to us by Olivier Dudas concerning unipotent supports.en_US
dc.description.sponsorshipINdAM (Istituto Nazionale di Alta Matematica Francesco Severi); European Commission via an INdAM Marie Curie Fellowship; University of Padova [CPDA125818/12, 60A01-4222/15]en_US
dc.language.isoenen_US
dc.publisherCambridge University Pressen_US
dc.rights© Edinburgh Mathematical Society 2018.en_US
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subjectroot dataen_US
dc.subjectsmooth regular embeddingsen_US
dc.subjectunipotent supportsen_US
dc.titleThe Structure of Root Data and Smooth Regular Embeddings of Reductive Groupsen_US
dc.typeArticleen_US
dc.contributor.departmentUniversity of Arizonaen_US
dc.identifier.journalProceedings of the Edinburgh Mathematical Societyen_US
dc.description.note6 month embargo; published online: 29 November 2018en_US
dc.description.collectioninformationThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.en_US
dc.eprint.versionFinal accepted manuscripten_US


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