Geodesic
Subgroups of the orthogonal groups of even degree over a local field
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 12, Tome 321 (2005), pp. 240-250 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

In this paper, we obtain the description of subgroups of orthogonal linear groups $\operatorname{SO}(2l,K)$ and $\operatorname{GO}(2l,K)$ over the field of fractions $K$ of a local principal ideal domain $R$ containing the maximal split tori $T=T(2l,R)$ with entries from $R$. Similar result for overgroups $T$ in case of semilocal ring and field was obtained earlier by N. Vavilov. Result of the present paper generalizes also some known results. 
@article{ZNSL_2005_321_a12,
     author = {K. Yu. Lavrov},
     title = {Subgroups of the orthogonal groups of even degree over a~local field},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {240--250},
     year = {2005},
     volume = {321},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2005_321_a12/}
}
TY  - JOUR
AU  - K. Yu. Lavrov
TI  - Subgroups of the orthogonal groups of even degree over a local field
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2005
SP  - 240
EP  - 250
VL  - 321
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2005_321_a12/
LA  - ru
ID  - ZNSL_2005_321_a12
ER  - 
%0 Journal Article
%A K. Yu. Lavrov
%T Subgroups of the orthogonal groups of even degree over a local field
%J Zapiski Nauchnykh Seminarov POMI
%D 2005
%P 240-250
%V 321
%U http://geodesic.mathdoc.fr/item/ZNSL_2005_321_a12/
%G ru
%F ZNSL_2005_321_a12
K. Yu. Lavrov. Subgroups of the orthogonal groups of even degree over a local field. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 12, Tome 321 (2005), pp. 240-250. http://geodesic.mathdoc.fr/item/ZNSL_2005_321_a12/

[1] Z. I. Borevich, “Opisanie podgrupp polnoi lineinoi gruppy, soderzhaschikh gruppu diagonalnykh matrits”, Zap. nauchn. semin. LOMI, 64, 1976, 12–29 | Zbl

[2] Z. I. Borevich, “O parabolicheskikh podgruppakh v spetsialnoi lineinoi gruppe nad polulokalnym koltsom”, Vestn. Leningr. Un-ta, 19 (1976), 29–34 | MR | Zbl

[3] Z. I. Borevich, N. A. Vavilov, “Podgruppy polnoi lineinoi gruppy nad polulokalnym koltsom, soderzhaschie gruppu diagonalnykh matrits”, Tr. Matem. in-ta AN SSSR, 148, 1978, 43–57 | MR | Zbl

[4] Z. I. Borevich, E. V. Dybkova, L. Yu. Kolotilina, “O sopryazhennosti setevykh podgrupp v lineinykh gruppakh”, Zap. nauchn. semin. LOMI, 86, 1979, 11–18 | MR | Zbl

[5] N. A. Vavilov, “O parabolicheskikh podgruppakh grupp Shevalle nad polulokalnym koltsom”, Zap. nauchn. semin. LOMI, 75, 1978, 43–58 | MR | Zbl

[6] N. A. Vavilov, “O podgruppakh polnoi lineinoi gruppy nad polulokalnym koltsom, soderzhaschikh gruppu diagonalnykh matrits”, Vestn. Leningr. un-ta, 1 (1981), 10–15 | MR | Zbl

[7] N. A. Vavilov, “Parabolicheskie podgruppy grupp Shevalle nad kommutativnym koltsom”, Zap. nauchn. semin. LOMI, 116, 1982, 20–43 | MR | Zbl

[8] N. A. Vavilov, “O podgruppakh spetsialnoi lineinoi gruppy, soderzhashikh gruppu diagonalnykh matrits, I–IV”, Vestn. Leningr. un-ta, Ser. I, 22 (1985), 3–7 ; 2:1 (1986), 10–15 ; 2 (1987), 3–8 ; 3 (1988), 10–15 | MR | Zbl | MR | MR | Zbl | MR | Zbl

[9] N. A. Vavilov, Subgroups of $\mathrm{SL}_n$ over a semilocal ring, Preprint Universität Bielefeld, No 111, 1998

[10] N. A. Vavilov, “O podgruppakh rasschepimykh ortogonalnykh grupp”, Sib. mat. zhurnal, 24 (1988), 12–25 | MR

[11] N. A. Vavilov, “Intermediate subgroups in Chevalley groups”, Proc. Conf. Groups of Lie type and their Geometries (Como, 1993), Cambridge Univ. Press, 1995, 233–280 | MR | Zbl

[12] N. A. Vavilov, I. Khamdan, “O podgruppakh polnoi lineinoi gruppy nad lokalnym polem”, Izv. vuzov. Matematika, 12 (1989), 8–15 | MR | Zbl

[13] K. Yu. Lavrov, “Podgruppy polnoi lineinoi gruppy nad lokalnym polem”, Zap. nauchn. semin. POMI, 272, 2000, 242–258 | MR | Zbl

[14] I. Khamdan, Podgruppy polnoi lineinoi gruppy nad polem chastnykh polulokalnogo koltsa, Kand. diss., Leningrad, 1987

[15] I. Khamdan, “O podgruppakh spetsialnoi lineinoi gruppy nad lokalnym koltsom glavnykh idealov”, Sb. nauchn. trudov. (Koltsa i lineinye gruppy), Kubanskii gos. un-t, 1988, 119–126 | MR