Quasi-split symmetric pairs of $U({\mathfrak{sl}}_n)$ and Steinberg varieties of classical type

Abstract

We provide a Lagrangian construction for the fixed-point subalgebra, together with its idempotent form, in a quasi-split symmetric pair of type $A_{n-1}$. This is obtained inside the limit of a projective system of Borel-Moore homologies of the Steinberg varieties of $n$-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.

arXiv commentSubstantial revision at the suggestions of the anonymous referee. Final version. To appear in Represent. Theory

References in corpus (1)

• Cohomology for quantum groups via the geometry of the nullcone