# Maximal subgroups of indefinite special orthogonal group SO(p,q)

Can someone answer the following question: Is there any classification of maximal proper Zariski-closed real subgroups of $SO(p,q)$ which are not parabolic, and satisfy the following conditions:

1. they have rank at least the rank of $SO(p) \times SO(q)$ .

2. they should act irreducibly on the natural representation of $SO(p,q)$, i.e. on $\mathbb{R}^{p,q}$.

Thanks.

• The references given in this answer classify all maximal subgroups; perhaps extracting the ones you want is not too hard? – Francois Ziegler Sep 20 '14 at 16:46
• Forgive me asking this: I tried to get the papers you suggested from my library, but I could not get them. Do you have access to them, and in case if they are allowed to be shared, would you please share them with me?. – user49908 Sep 20 '14 at 22:42
• Sorry, I don't have copies at hand; have you tried interlibrary loan? – Francois Ziegler Sep 21 '14 at 0:36
• @Francois: The paper by Taufik contains classification of irreducible maximal subalgebras. In that paper, he mentions that the reducible ones are given in mathnet.ru/php/… – user49908 Sep 28 '14 at 3:38
• I'm afraid Mušic's paper hasn't been translated. OTOH, you should be able to find translations of Dynkin's, in "Selected papers of E. B. Dynkin with commentary". – Francois Ziegler Sep 28 '14 at 5:30

A Russian mathematician whose name is Komrakov, has listed the maximal subgroups of SO(p,q), if you do not find the articles, i have the pdf fil's, best regards jorge

• Note that the key paper by Komrakov is one of the references mentioned by Francois, though it lacks full details. The basic source is the older classification work by Dynkin. – Jim Humphreys Sep 26 '14 at 18:09
• Thanks to Francois, I found the references. The paper by Komrakov contains final results at the Lie algebra level. If you have the papers that have proofs, please send it to me. – user49908 Sep 27 '14 at 17:25