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

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- by Yiqiang Li
- Represent. Theory
**25**(2021), 903-934 - DOI: https://doi.org/10.1090/ert/570
- Published electronically: October 21, 2021
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## 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.## References

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## Bibliographic Information

**Yiqiang Li**- Affiliation: Department of Mathematics, University at Buffalo, The State University of New York, 244 Mathematics Building, Buffalo, New York 14260
- MR Author ID: 828279
- ORCID: 0000-0003-4608-3465
- Email: yiqiang@buffalo.edu
- Received by editor(s): January 17, 2020
- Received by editor(s) in revised form: February 7, 2021
- Published electronically: October 21, 2021
- Additional Notes: This work was partially supported by the NSF grant DMS-1801915.
- © Copyright 2021 American Mathematical Society
- Journal: Represent. Theory
**25**(2021), 903-934 - MSC (2020): Primary 17B35, 51N30
- DOI: https://doi.org/10.1090/ert/570
- MathSciNet review: 4329193