We provide a Lagrangian construction for the fixed-point subalgebra, together with its idempotent form, in a quasi-split symmetric pair of type A n − 1 A_{n-1} . This is obtained inside the limit of a projective system of Borel-Moore homologies of the Steinberg varieties of n n -step isotropic flag varieties. Arising from the construction are a basis of homological origin for the idempotent form and a geometric realization of rational modules.

中文翻译：

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经典类型的 𝑈(𝔰𝔩_{𝔫}) 和 Steinberg 变体的拟分裂对称对

我们在 A n − 1 A_{n-1} 类型的准分裂对称对中为定点子代数及其幂等形式提供了拉格朗日构造。这是在 nn 阶各向同性标志变体的 Steinberg 变体的 Borel-Moore 同调射影系统的极限内获得的。由构造产生的是幂等形式的同调起源基础和有理模块的几何实现。