arXiv:2302.09329 Abstract | arXiv Analytics

arXiv:2302.09329 [math.RT]Abstract References Reviews Resources

Zigzag algebras and faithfulness of the 2-braid groups in type B

Published 2023-02-18Version 1

We show that certain category of bimodules over a finite dimensional quiver algebra known as type B zigzag algebra is a quotient category of the category of type B Soergel bimodules. This leads to an alternate proof of Rouquier's conjecture on the faithfulness of the 2-braid groups for type B.

Comments: 15 pages. Split from an earlier paper following referee suggestion. Comments welcomed!

Categories: math.RT, math.QA

Subjects: 20F36, 20J05, 20C08

Keywords: zigzag algebra, faithfulness, finite dimensional quiver algebra, quotient category, soergel bimodules

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