Decomposition of transvections: An algebro-geometric approach
Author:
V. Petrov
Translated by:
The AUTHOR
Original publication:
Algebra i Analiz, tom 28 (2016), nomer 1.
Journal:
St. Petersburg Math. J. 28 (2017), 109-114
MSC (2010):
Primary 20G35
DOI:
https://doi.org/10.1090/spmj/1440
Published electronically:
November 30, 2016
MathSciNet review:
3591068
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: A simple and uniform algebro-geometric proof is given for the decomposition of transvections for Chevalley groups in minuscule representations.
- Patrick Brosnan, On motivic decompositions arising from the method of Białynicki-Birula, Invent. Math. 161 (2005), no. 1, 91–111. MR 2178658, DOI https://doi.org/10.1007/s00222-004-0419-7
- Vladimir Chernousov, Stefan Gille, and Alexander Merkurjev, Motivic decomposition of isotropic projective homogeneous varieties, Duke Math. J. 126 (2005), no. 1, 137–159. MR 2110630, DOI https://doi.org/10.1215/S0012-7094-04-12614-4
- Alexei Stepanov and Nikolai Vavilov, Decomposition of transvections: a theme with variations, $K$-Theory 19 (2000), no. 2, 109–153. MR 1740757, DOI https://doi.org/10.1023/A%3A1007853629389
- Nikolai Vavilov, A third look at weight diagrams, Rend. Sem. Mat. Univ. Padova 104 (2000), 201–250. MR 1809357
- Nikolai A. Vavilov, Structure of Chevalley groups over commutative rings, Nonassociative algebras and related topics (Hiroshima, 1990) World Sci. Publ., River Edge, NJ, 1991, pp. 219–335. MR 1150262
- ---, Decomposition of unipotents for $\mathrm E_6$ and $\mathrm E_7$: $25$ years after, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 430 (2014), 32–52. (Russian)
- Nikolai Vavilov and Eugene Plotkin, Chevalley groups over commutative rings. I. Elementary calculations, Acta Appl. Math. 45 (1996), no. 1, 73–113. MR 1409655, DOI https://doi.org/10.1007/BF00047884
- N. A. Vavilov and M. R. Gavrilovich, $A_2$-proof of structure theorems for Chevalley groups of types $E_6$ and $E_7$, Algebra i Analiz 16 (2004), no. 4, 54–87 (Russian, with Russian summary); English transl., St. Petersburg Math. J. 16 (2005), no. 4, 649–672. MR 2090851, DOI https://doi.org/10.1090/S1061-0022-05-00871-X
- N. A. Vavilov, M. R. Gavrilovich, and S. I. Nikolenko, The structure of Chevalley groups: a proof from The Book, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 330 (2006), no. Vopr. Teor. Predst. Algebr. i Grupp. 13, 36–76, 271–272 (Russian, with English and Russian summaries); English transl., J. Math. Sci. (N.Y.) 140 (2007), no. 5, 626–645. MR 2253566, DOI https://doi.org/10.1007/s10958-007-0003-y
- N. A. Vavilov and V. G. Kazakevich, Decomposition of transvections for automorphisms, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 365 (2009), no. Voprosy Teorii Predstavleniĭ Algebr i Grupp. 18, 47–62, 262–263 (Russian, with English and Russian summaries); English transl., J. Math. Sci. (N.Y.) 161 (2009), no. 4, 483–491. MR 2749134, DOI https://doi.org/10.1007/s10958-009-9578-9
- N. A. Vavilov and V. G. Kazakevich, More variations on the decomposition of transvections, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 375 (2010), no. Voprosy Teorii Predstavleniĭ Algebr i Grupp. 19, 32–47, 209–210 (Russian, with English and Russian summaries); English transl., J. Math. Sci. (N.Y.) 171 (2010), no. 3, 322–330. MR 2749273, DOI https://doi.org/10.1007/s10958-010-0137-1
- N. A. Vavilov and A. K. Stavrova, Basic reductions in the problem of the description of normal subgroups, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 349 (2007), no. Voprosy Teorii Predstavleniĭ Algebr i Grupp. 16, 30–52, 242–243 (Russian, with English and Russian summaries); English transl., J. Math. Sci. (N.Y.) 151 (2008), no. 3, 2949–2960. MR 2742853, DOI https://doi.org/10.1007/s10958-008-9019-1
Retrieve articles in St. Petersburg Mathematical Journal with MSC (2010): 20G35
Retrieve articles in all journals with MSC (2010): 20G35
Additional Information
V. Petrov
Affiliation:
St. Petersburg State University, Chebyshev Laboratory, 29B 14th line V.O., 199178 St. Petersburg, Russia
Email:
victorapetrov@googlemail.com
Keywords:
Decomposition of unipotents,
minuscule representations
Received by editor(s):
July 24, 2015
Published electronically:
November 30, 2016
Additional Notes:
This work is supported by Russian Science Foundation, grant 14-11-00297
Article copyright:
© Copyright 2016
American Mathematical Society