**BILKENT **

**FUSION SYSTEMS
SEMINAR**

**"Fusion
Systems of Blocks: Part II"**

By

# LAURENCE BARKER

# (Bilkent University)

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**Abstract: ****The objects of the fusion system of a block b can usefully be identified with the Brauer pairs containing (1, b). Recall, the inclusion relation between Brauer pairs is awkward to describe directly. A more elegant description of the inclusion relation can be expressed by passing to a refinement of the fusion system, called the Puig category. Instead of pairs (P, e) where e is a block of FC(P), the objects of the Puig category have the form (P, c), where c is a point of P on FG, equivalently, c is a simple FC(P)-module. Interestingly, all the objects in the Puig category have associated twists, not just the centric objects. We shall examine the Puig categories of the principal 2-blocks of D8, S4 and A6.**

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**Date: ****Tuesday, November 3, 2015**

**Time: ****15.40**

**Place: ****Mathematics Seminar Room,
SA-141**

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**All are most cordially invited.**