Matching Tag: diagonal-actions
Let X d = S L d ( R ) / S L d ( Z ) X_d=\mathrm{SL}_d(\mathbb{R})/\mathrm{SL}_d(\mathbb{Z}) X d = SL d ( R ) / SL d ( Z ) and let A A A be the connected diagonal subgroup … An A A A -orbit is bounded if its image in X d X_d X d is bounded. Margulis' c…
Stable-perturbation conjecture. For every open cone C ⊆ a C\subseteq\mathfrak{a} C ⊆ a , every bounded A C A_C A C -orbit in X d X_d X d contains an A C A_C A C -stable perturbation of a compact A A A -orbit. This…
Let d ≥ 3 d\geq 3 d ≥ 3 , let X d = S L d ( R ) / S L d ( Z ) X_d=\mathrm{SL}_d(\mathbb{R})/\mathrm{SL}_d(\mathbb{Z}) X d = SL d ( R ) / SL d ( Z ) , and let I m , J n I_m,J_n I m , J n be index sets. Choose nonzero vectors…
Let d ≥ 3 d\geq 3 d ≥ 3 , let X d = S L d ( R ) / S L d ( Z ) X_d=\mathrm{SL}_d(\mathbb{R})/\mathrm{SL}_d(\mathbb{Z}) X d = SL d ( R ) / SL d ( Z ) , and let v 1 ≠ v 2 v^1\ne v^2 v 1 = v 2 be two nonzero vectors in the diagonal subalgebra of…
Let D D D be the diagonal group of SL n ( R ) \operatorname{SL}_n(\mathbb{R}) SL n ( R ) where n ≥ 3 n\ge 3 n ≥ 3 . A D D D -orbit in SL n ( R ) / SL n ( Z ) \operatorname{SL}_n(\mathbb{R})/\operatorname{SL}_n(\mathbb{Z}) SL n ( R ) / SL n ( Z ) is relatively co…