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-Conjugacy classes in loop groups
Author:
Dongwen Liu
Journal:
Proc. Amer. Math. Soc. 140 (2012), 3297-3311
MSC (2010):
Primary 22E67
Posted:
January 31, 2012
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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.
References
- 1.
M.
F. Atiyah, Vector bundles over an elliptic curve, Proc. London
Math. Soc. (3) 7 (1957), 414–452. MR 0131423
(24 #A1274)
- 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
(97j:20044), http://dx.doi.org/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
(38 #4271a)
- 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 (94j:17001)
- 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
(20 #4608)
- 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
(2005a:12013), http://dx.doi.org/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
(51 #509)
- 9.
Nicholas
M. Katz, A simple algorithm for cyclic vectors, Amer. J. Math.
109 (1987), no. 1, 65–70. MR 878198
(88b:13001), http://dx.doi.org/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
(28 #1200)
- 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
(2009d:39033)
- 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
(2001m:39043)
- 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
(2006d:39031)
- 14.
Jean-Pierre
Serre, Local fields, Graduate Texts in Mathematics,
vol. 67, Springer-Verlag, New York, 1979. Translated from the French
by Marvin Jay Greenberg. MR 554237
(82e:12016)
- 15.
John
T. Tate, The arithmetic of elliptic curves, Invent. Math.
23 (1974), 179–206. MR 0419359
(54 #7380)
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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
Email:
math.dwliu@gmail.com
DOI:
http://dx.doi.org/10.1090/S0002-9939-2012-11213-4
PII:
S 0002-9939(2012)11213-4
Keywords:
Loop groups,
conjugacy classes
Received by editor(s):
December 2, 2010
Received by editor(s) in revised form:
March 30, 2011
Posted:
January 31, 2012
Communicated by:
Lev Borisov
Article copyright:
© Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain after
28 years from publication.
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