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JOURNALS // Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika // Archive

Izv. Vyssh. Uchebn. Zaved. Mat., 2017 Number 11, Pages 68–77 (Mi ivm9302)

On coset-spaces of compact Lie groups by subgrops of corank two

A. N. Shchetinin

Bauman Moscow State Technical University, 5 Vtoraya Baumanskaya str., Moscow, 105005 Russia

Abstract: Let $G$ and $G'$ be compact connected simply connected Lie groups. Suppose that $G$ is a simple group, $L$ is a centralizer of torus of $G$, $H$ is the commutant of the subgroup $L$, and $\mathrm{rk}~G - \mathrm{rk}~H = 2$. Let $\mathrm{Sam}~(G/H) = 0$. We prove the following assertion: if the group $G'$ acts transitively and almost effectively on the manifold $G/H$, then $G' \cong G$. If all lenghts of roots of the group $G$ are equal, then the action of $G'$ on $G/H$ is similar to the action of $G$.

Keywords: compact Lie group, cohomology, homotopy groups, transitive action.

UDC: 512.816

Received: 23.06.2016


 English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2017, 61:11, 60–68

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© Steklov Math. Inst. of RAS, 2025