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$ q$-Conjugacy classes in loop groups

Author: Dongwen Liu
Journal: Proc. Amer. Math. Soc. 140 (2012), 3297-3311
MSC (2010): Primary 22E67
Published electronically: January 31, 2012
MathSciNet review: 2917102
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Abstract: This paper discusses the twisted conjugacy classes in loop groups. We restrict to classical groups and give some explicit classifications.

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  • 1. M. F. Atiyah, Vector bundles over an elliptic curve, Proc. London Math. Soc. (3) 7 (1957), 414–452. MR 0131423
  • 2. Vladimir Baranovsky and Victor Ginzburg, Conjugacy classes in loop groups and 𝐺-bundles on elliptic curves, Internat. Math. Res. Notices 15 (1996), 733–751. MR 1413870, 10.1155/S1073792896000463
  • 3. George David Birkhoff, Collected mathematical papers (in three volumes). Vol. I: Boundary value problems and associated Sturmian problems, differential equations, difference equations, dynamics (partial), Editorial committee: D. V. Widder (Chairman), C. R. Adams, R. E. Langer, Marston Morse and M. H. Stone, Dover Publications, Inc., New York, 1968. MR 0235971
  • 4. David H. Collingwood and William M. McGovern, Nilpotent orbits in semisimple Lie algebras, Van Nostrand Reinhold Mathematics Series, Van Nostrand Reinhold Co., New York, 1993. MR 1251060
  • 5. Jean Dieudonné, Groupes de Lie et hyperalgèbres de Lie sur un corps de caractéristique 𝑝>0. VII, Math. Ann. 134 (1957), 114–133 (French). MR 0098146
  • 6. Lucia Di Vizio, Arithmetic theory of 𝑞-difference equations: the 𝑞-analogue of Grothendieck-Katz’s conjecture on 𝑝-curvatures, Invent. Math. 150 (2002), no. 3, 517–578. MR 1946552, 10.1007/s00222-002-0241-z
  • 7. R. Friedman, J. W. Morgan, Holomorphic principal bundles over elliptic curves, arXiv: math/9811130.
  • 8. G. Harder and M. S. Narasimhan, On the cohomology groups of moduli spaces of vector bundles on curves, Math. Ann. 212 (1974/75), 215–248. MR 0364254
  • 9. Nicholas M. Katz, A simple algorithm for cyclic vectors, Amer. J. Math. 109 (1987), no. 1, 65–70. MR 878198, 10.2307/2374551
  • 10. Ju. I. Manin, Theory of commutative formal groups over fields of finite characteristic, Uspehi Mat. Nauk 18 (1963), no. 6 (114), 3–90 (Russian). MR 0157972
  • 11. Marius van der Put and Marc Reversat, Galois theory of 𝑞-difference equations, Ann. Fac. Sci. Toulouse Math. (6) 16 (2007), no. 3, 665–718 (English, with English and French summaries). MR 2379057
  • 12. Jacques Sauloy, Systèmes aux 𝑞-différences singuliers réguliers: classification, matrice de connexion et monodromie, Ann. Inst. Fourier (Grenoble) 50 (2000), no. 4, 1021–1071 (French, with English and French summaries). MR 1799737
  • 13. Jacques Sauloy, La filtration canonique par les pentes d’un module aux 𝑞-différences et le gradué associé, Ann. Inst. Fourier (Grenoble) 54 (2004), no. 1, 181–210 (French, with English and French summaries). MR 2069126
  • 14. Jean-Pierre Serre, Local fields, Graduate Texts in Mathematics, vol. 67, Springer-Verlag, New York-Berlin, 1979. Translated from the French by Marvin Jay Greenberg. MR 554237
  • 15. John T. Tate, The arithmetic of elliptic curves, Invent. Math. 23 (1974), 179–206. MR 0419359

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Additional Information

Dongwen Liu
Affiliation: Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
Address at time of publication: School of Mathematical Science, Xiamen University, Xiamen, Fujian, People’s Republic of China

Keywords: Loop groups, conjugacy classes
Received by editor(s): December 2, 2010
Received by editor(s) in revised form: March 30, 2011
Published electronically: January 31, 2012
Communicated by: Lev Borisov
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.