Distinguished strata in a reductive group

Lusztig, G.

doi:10.1090/ert/619

Distinguished strata in a reductive group
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by G. Lusztig

Represent. Theory 26 (2022), 698-713

DOI: https://doi.org/10.1090/ert/619

Published electronically: June 30, 2022

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Abstract:

The set of strata of a reductive group can be viewed as an enlargement of the set of unipotent classes. In this paper the notion of distinguished unipotent class is extended to this larger set. The strata of a Weyl group are also introduced and studied.

References

P. Bala and R. W. Carter, Classes of unipotent elements in simple algebraic groups. I, Math. Proc. Cambridge Philos. Soc. 79 (1976), no. 3, 401–425. MR 417306, DOI 10.1017/S0305004100052403
Giovanna Carnovale, Lusztig’s strata are locally closed, Arch. Math. (Basel) 115 (2020), no. 1, 23–26. MR 4105009, DOI 10.1007/s00013-020-01448-1
R. W. Carter, Conjugacy classes in the Weyl group, Compositio Math. 25 (1972), 1–59. MR 318337
Martin W. Liebeck and Gary M. Seitz, Unipotent and nilpotent classes in simple algebraic groups and Lie algebras, Mathematical Surveys and Monographs, vol. 180, American Mathematical Society, Providence, RI, 2012. MR 2883501, DOI 10.1090/surv/180
G. Lusztig, Intersection cohomology complexes on a reductive group, Invent. Math. 75 (1984), no. 2, 205–272. MR 732546, DOI 10.1007/BF01388564
G. Lusztig, From conjugacy classes in the Weyl group to unipotent classes, Represent. Theory 15 (2011), 494–530. MR 2833465, DOI 10.1090/S1088-4165-2011-00396-4
G. Lusztig, On $C$-small conjugacy classes in a reductive group, Transform. Groups 16 (2011), no. 3, 807–825. MR 2827045, DOI 10.1007/s00031-011-9145-6
G. Lusztig, From conjugacy classes in the Weyl group to unipotent classes, II, Represent. Theory 16 (2012), 189–211. MR 2904567, DOI 10.1090/S1088-4165-2012-00411-3
George Lusztig, On conjugacy classes in a reductive group, Representations of reductive groups, Progr. Math., vol. 312, Birkhäuser/Springer, Cham, 2015, pp. 333–363. MR 3495802, DOI 10.1007/978-3-319-23443-4_{1}2
G. Lusztig, Strata of a disconnected reductive group, Indag. Math. (N.S.) 32 (2021), no. 5, 968–986. MR 4310009, DOI 10.1016/j.indag.2020.09.011
Kenzo Mizuno, The conjugate classes of unipotent elements of the Chevalley groups $E_{7}$ and $E_{8}$, Tokyo J. Math. 3 (1980), no. 2, 391–461. MR 605099, DOI 10.3836/tjm/1270473003
G. E. Wall, On the conjugacy classes in the unitary, symplectic and orthogonal groups, J. Austral. Math. Soc. 3 (1963), 1–62. MR 0150210, DOI 10.1017/S1446788700027622
Zhiwei Yun, Minimal reduction type and the Kazhdan-Lusztig map, Indag. Math. (N.S.) 32 (2021), no. 6, 1240–1274. MR 4334167, DOI 10.1016/j.indag.2021.06.007