Geometric Schur duality of classical type, II
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- by Zhaobing Fan and Yiqiang Li HTML | PDF
- Trans. Amer. Math. Soc. Ser. B 2 (2015), 51-92
Abstract:
We establish algebraically and geometrically a duality between the Iwahori-Hecke algebra of type $\mathbf D$ and two new quantum algebras arising from the geometry of $N$-step isotropic flag varieties of type $\mathbf D$. This duality is a type $\mathbf D$ counterpart of the Schur-Jimbo duality of type $\mathbf A$ and the Schur-like duality of type $\mathbf B/\mathbf C$ discovered by Bao-Wang. The new algebras play a role in the type $\mathbf D$ duality similar to the modified quantum $\mathfrak {gl}(N)$ in type $\mathbf A$, and the modified coideal subalgebras of quantum $\mathfrak {gl}(N)$ in type $\mathbf B/\mathbf C$. We construct canonical bases for these two algebras.References
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Additional Information
- Zhaobing Fan
- Affiliation: Department of Mathematics, Kansas State University, Manhattan, Kansas 66506
- Address at time of publication: School of Science, Harbin Engineering University, Harbin 150001, People’s Republic of China
- MR Author ID: 684558
- Email: fanz@math.ksu.edu
- Yiqiang Li
- Affiliation: Department of Mathematics, University at Buffalo, SUNY, Buffalo, New York 14260
- MR Author ID: 828279
- ORCID: 0000-0003-4608-3465
- Email: yiqiang@buffalo.edu
- Received by editor(s): December 15, 2014
- Received by editor(s) in revised form: September 7, 2015
- Published electronically: September 30, 2015
- © Copyright 2015 by the authors under Creative Commons Attribution-Noncommercial 3.0 License (CC BY NC 3.0)
- Journal: Trans. Amer. Math. Soc. Ser. B 2 (2015), 51-92
- MSC (2010): Primary 17B37, 14L35, 20G43
- DOI: https://doi.org/10.1090/btran/8
- MathSciNet review: 3402700