Twisted quadratic foldings of root systems
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- by M. Lanini and K. Zainoulline
- St. Petersburg Math. J. 33 (2022), 65-84
- DOI: https://doi.org/10.1090/spmj/1690
- Published electronically: December 28, 2021
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Abstract:
The present paper is devoted to twisted foldings of root systems that generalize the involutive foldings corresponding to automorphisms of Dynkin diagrams. A motivating example is Lusztig’s projection of the root system of type $E_8$ onto the subring of icosians of the quaternion algebra, which gives the root system of type $H_4$.
By using moment graph techniques for any such folding, a map at the equivariant cohomology level is constructed. It is shown that this map commutes with characteristic classes and Borel maps. Restrictions of this map to the usual cohomology of projective homogeneous varieties, to group cohomology and to their virtual analogues for finite reflection groups are also introduced and studied.
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Bibliographic Information
- M. Lanini
- Affiliation: Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica, 00133 Rome, Italy
- MR Author ID: 990628
- Email: lanini@mat.uniroma2.it
- K. Zainoulline
- Affiliation: Department of Mathematics and Statistics, University of Ottawa, 585 King Edward Street, Ottawa, ON, K1N 6N5, Canada
- MR Author ID: 662935
- ORCID: 0000-0002-9591-0634
- Email: kirill@uottawa.ca
- Received by editor(s): February 28, 2020
- Published electronically: December 28, 2021
- Additional Notes: M. L. acknowledges the MIUR Excellence Department Project awarded to the Department of Mathematics, University of Rome Tor Vergata, CUPE83C18000100006, and the PRIN2017 CUPE84-1900048000. K. Z. was partially supported by the NSERC Discovery grant RGPIN-2015-04469, Canada
- © Copyright 2021 American Mathematical Society
- Journal: St. Petersburg Math. J. 33 (2022), 65-84
- MSC (2020): Primary 14M15, 17B22, 20G41
- DOI: https://doi.org/10.1090/spmj/1690
- MathSciNet review: 4219506