Integration of modules – II: Exponentials

Rumynin, Dmitriy; Westaway, Matthew

doi:10.1090/tran/8449

Integration of modules – II: Exponentials
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Trans. Amer. Math. Soc. 374 (2021), 6797-6813 Request permission

Abstract:

We continue our exploration of various approaches to integration of representations from a Lie algebra $\mathrm {Lie} (G)$ to an algebraic group $G$ in positive characteristic. In the present paper we concentrate on an approach exploiting exponentials. This approach works well for over-restricted representations, introduced in this paper, and takes no note of $G$-stability.

References

John W. Ballard, Injective modules for restricted enveloping algebras, Math. Z. 163 (1978), no. 1, 57–63. MR 510324, DOI 10.1007/BF01214444
Armand Borel, Linear algebraic groups, 2nd ed., Graduate Texts in Mathematics, vol. 126, Springer-Verlag, New York, 1991. MR 1102012, DOI 10.1007/978-1-4612-0941-6
R. W. Carter and Y. Chen, Automorphisms of affine Kac-Moody groups and related Chevalley groups over rings, J. Algebra 155 (1993), no. 1, 44–94. MR 1206622, DOI 10.1006/jabr.1993.1031
Stephen Donkin, A note on the characters of the projective modules for the infinitesimal subgroups of a semisimple algebraic group, Math. Scand. 51 (1982), no. 1, 142–150. MR 681263, DOI 10.7146/math.scand.a-11968
J. E. Humphreys and D. N. Verma, Projective modules for finite Chevalley groups, Bull. Amer. Math. Soc. 79 (1973), 467–468. MR 320176, DOI 10.1090/S0002-9904-1973-13220-3
James E. Humphreys, Introduction to Lie algebras and representation theory, Graduate Texts in Mathematics, Vol. 9, Springer-Verlag, New York-Berlin, 1972. MR 0323842
Jens C. Jantzen, Darstellungen halbeinfacher Gruppen und ihrer Frobenius-Kerne, J. Reine Angew. Math. 317 (1980), 157–199 (German). MR 581341, DOI 10.1515/crll.1980.317.157
Jens Carsten Jantzen, Representations of algebraic groups, Pure and Applied Mathematics, vol. 131, Academic Press, Inc., Boston, MA, 1987. MR 899071
Tetsuzo Kimura and Hiroshi Niitsuma, On Kunz’s conjecture, J. Math. Soc. Japan 34 (1982), no. 2, 371–378. MR 651278, DOI 10.2969/jmsj/03420371
Ernst Kunz, Kähler differentials, Advanced Lectures in Mathematics, Friedr. Vieweg & Sohn, Braunschweig, 1986. MR 864975, DOI 10.1007/978-3-663-14074-0
T. Marquis, Topological Kac-Moody groups and their subgroups, Ph.D. Thesis, Universite Catholique de Louvain, 2013.
Bertrand Rémy, Groupes de Kac-Moody déployés et presque déployés, Astérisque 277 (2002), viii+348 (French, with English and French summaries). MR 1909671
Guy Rousseau, Groupes de Kac-Moody déployés sur un corps local II. Masures ordonnées, Bull. Soc. Math. France 144 (2016), no. 4, 613–692 (French, with English and French summaries). MR 3562609, DOI 10.24033/bsmf.2724
D. Rumynin, Kac-Moody groups and their representations, In: New trends in algebras and combinatorics, Proceedings of the 3rd International Congress in Algebras and Combinatorics (ICAC2017), World Scientific, 2020.
Dmitriy Rumynin and Matthew Westaway, Integration of modules I: stability, Pacific J. Math. 301 (2019), no. 2, 575–600. MR 4023359, DOI 10.2140/pjm.2019.301.575
I. R. Shafarevich, Basic algebraic geometry, Springer Study Edition, Springer-Verlag, Berlin-New York, 1977. Translated from the Russian by K. A. Hirsch; Revised printing of Grundlehren der mathematischen Wissenschaften, Vol. 213, 1974. MR 0447223
Paul Sobaje, On liftings of projective indecomposable $G_{(1)}$-modules, J. Algebra 475 (2017), 61–79. MR 3612464, DOI 10.1016/j.jalgebra.2016.10.021
Jacques Tits, Uniqueness and presentation of Kac-Moody groups over fields, J. Algebra 105 (1987), no. 2, 542–573. MR 873684, DOI 10.1016/0021-8693(87)90214-6
B. Ju. Veĭsfeĭler and V. G. Kac, Exponentials in Lie algebras of characteristic $p$, Izv. Akad. Nauk SSSR Ser. Mat. 35 (1971), 762–788 (Russian). MR 0306282

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Integration of modules – II: Exponentials
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Abstract: