Faithfulness of the 2-Braid Group via Zigzag Algebra in Type B

Abstract

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.

20 pages. Split from an earlier paper following referee suggestion. Minor corrections following referee suggestion. To appear in JAustMS

References in corpus (2)

• The Burau representation is not faithful for n = 5
• Curves in the disc, the type B braid group, and the type B zigzag algebra