Geometric Schur duality of classical type, II

Fan, Zhaobing; Li, Yiqiang

doi:10.1090/btran/8

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.

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