Geometric Schur Duality of Classical Type View Full Text


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Article Info

DATE

2018-06

AUTHORS

Huanchen Bao, Jonathan Kujawa, Yiqiang Li, Weiqiang Wang

ABSTRACT

This is a generalization of the classic work of Beilinson, Lusztig and MacPherson. In this paper (and an Appendix) we show that the quantum algebras obtained via a BLM-type stabilization procedure in the setting of partial Flag varieties of type B/C are two (modified) coideal subalgebras of the quantum general linear Lie algebra, U.ℐ and U.ʅ . We provide a geometric realization of the Schur-type duality of Bao–Wang between such a coideal algebra and Iwahori–Hecke algebra of type B. The monomial bases and canonical bases of the Schur algebras and the modified coideal algebra U.ℐ are constructed. In an Appendix by three authors, a more subtle 2-step stabilization procedure leading to U.ʅ is developed, and then monomial and canonical bases of U.ʅ are constructed. It is shown that U.ʅ is a subquotient of U.ℐ with compatible canonical bases. Moreover, a compatibility between canonical bases for modified coideal algebras and Schur algebras is established. More... »

PAGES

329-389

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00031-017-9447-4

DOI

http://dx.doi.org/10.1007/s00031-017-9447-4

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https://app.dimensions.ai/details/publication/pub.1092444655


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