Let G be one of the ind-groups GL(∞), O(∞), Sp(∞), and let P₁, ..., P_ℓ be an arbitrary set of ℓ splitting parabolic subgroups of G. We determine all such sets with the property that G acts with finitely many orbits on the ind-variety X₁ × × X_ℓ where X_i = G/P_i. In the case of a finite-dimensional classical linear algebraic group G, the analogous problem has been solved in a sequence of papers of Littelmann, Magyar–Weyman–Zelevinsky and Matsuki. An essential difference from the finite-dimensional case is that already for ℓ = 2, the condition that G acts on X₁ × X₂ with finitely many orbits is a rather restrictive condition on the pair P₁, P₂. We describe this condition explicitly. Using the description we tackle the most interesting case where ℓ = 3, and present the answer in the form of a table. For ℓ ≥ 4 there always are infinitely many G-orbits on X₁ × × X_ℓ.

让摹是IND-群体之一GL（∞），O（∞），SP（∞），并且让P ₁，...，P _ℓ是ℓ分裂抛物线分组的任意一组摹。我们确定所有这样的设置与属性，ģ与对IND-品种有限多个轨道X作用₁ ×× X _ℓ其中X_我= g ^ / P_我。在有限维经典线性代数群G的情况下，类似的问题已在Littelmann，Magyar–Weyman–Zelevinsky和Matsuki的一系列论文中得到解决。与有限维情况的本质区别是，对于ℓ = 2，G在有限的轨道上作用于X ₁ × X _2的条件是对P ₁，P _2的限制性条件。我们明确描述这种情况。使用描述，我们解决了最有趣的情况，即ℓ = 3，并以表格的形式给出了答案。对于ℓ≥4，X ₁ ××上总是有无限多的G轨道X _ℓ。