Geodesic
Double cosets of stabilizers of totally isotropic subspaces in a special unitary group II
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 32, Tome 460 (2017), pp. 82-113 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

In the article (N. Gordeev and U. Rehmann. Double cosets of stabilizers of totally isotropic subspaces in a special unitary group I, Zapiski Nauch. Sem. POMI, v. 452 (2016), 86–107) we have considered the decomposition $\mathrm{SU}(D,h)=\cup_iP_u\gamma_iP_v$ where $\mathrm{SU}(D,h)$ is a special unitary group over a division algebra $D$ with an involution, $h$ is a symmetric or skew symmetric non-degenerated Hermitian form, and $P_u,P_v$ are stabilizers of totally isotropic subspaces of the unitary space. Since $\Gamma=\mathrm{SU}(D,h)$ is a point group of a classical algebraic group $\widetilde\Gamma$ there is the “order of adherence” on the set of double cosets $\{P_u\gamma_iP_v\}$ which is induced by the Zariski topology on $\Gamma$. In the current paper we describe the adherence of such double cosets for the cases when $\widetilde\Gamma$ is an orthogonal or a symplectic group (that is, for groups of types $B_r,C_r,D_r$). 
@article{ZNSL_2017_460_a3,
     author = {N. Gordeev and U. Rehmann},
     title = {Double cosets of stabilizers of totally isotropic subspaces in a~special unitary {group~II}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {82--113},
     year = {2017},
     volume = {460},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_460_a3/}
}
TY  - JOUR
AU  - N. Gordeev
AU  - U. Rehmann
TI  - Double cosets of stabilizers of totally isotropic subspaces in a special unitary group II
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2017
SP  - 82
EP  - 113
VL  - 460
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2017_460_a3/
LA  - en
ID  - ZNSL_2017_460_a3
ER  - 
%0 Journal Article
%A N. Gordeev
%A U. Rehmann
%T Double cosets of stabilizers of totally isotropic subspaces in a special unitary group II
%J Zapiski Nauchnykh Seminarov POMI
%D 2017
%P 82-113
%V 460
%U http://geodesic.mathdoc.fr/item/ZNSL_2017_460_a3/
%G en
%F ZNSL_2017_460_a3
N. Gordeev; U. Rehmann. Double cosets of stabilizers of totally isotropic subspaces in a special unitary group II. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 32, Tome 460 (2017), pp. 82-113. http://geodesic.mathdoc.fr/item/ZNSL_2017_460_a3/

[1] N. Bourbaki, Éléments de Mathématique, Algebre Chapitres I–III, Herman, Paris, 1956 ; Chapitres VII–IX, Hermann, Paris, 1962 | MR | Zbl

[2] R. W. Carter, Finite Groups of Lie Type. Conjugacy classes and comlex characters, John Wiley and Sons, 1985 | MR

[3] N. Gordeev, U. Rehmann, “On linearly Kleiman groups”, Transform. Groups, 18:3 (2013), 685–709 | DOI | MR | Zbl

[4] N. Gordeev, U. Rehmann, “Double cosets of stabilizers of totally isotropic subspaces in a special unitary group. I”, Zap. Nauchn. Semin. POMI, 452, 2016, 86–107 | MR

[5] M.-A. Knuss, A. Merkurjev, M. Rost, J.-P. Tignol, The book of involutions, AMS Colloquium Publications, 44, 1998 | MR

[6] V. Platonov, A. Rapinchuk, Algebraic Groups and Number Theory, Academic Press, 1993 | MR

[7] Linear algebraic groups, T. A. Springer, 9, Second edition, Boston, 1998 | MR | Zbl

[8] J. Tits, “Classification of algebraic semisimple groups”, Proc. Symp. Pure Math., 9 (1966), 33–62 | DOI | MR | Zbl