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Lie Group Quantum Mathematics Seminar

Fusion Algebras for Twisted Affine Lie Algebras

Alejandro Ginory, Rutgers University

Location:  Hill 423
Date & time: Friday, 26 October 2018 at 2:00PM - 3:00PM

 Abstract:    In the category of integrable highest weight modules for affine Lie algebras, the usual tensor product fails to preserve the so-called level (i.e., the scalar action of the canonical central element). For untwisted affine Lie algebras, a product structure called the fusion product makes the subcategory of modules at a fixed positive integral level into a symmetric monoidal category (in particular, with non-negative integral structure constants). In this talk, I will introduce a fusion product with integral structure constants on the space of characters of twisted affine Lie algebras that generalizes the untwisted case. Surprisingly, in the A^(2)_{2n} case and for certain natural quotients for the other twisted cases, these algebras have negative structure constants "half" the time, (depending on the parity of the level). We will discuss these and other new features in the twisted cases, and their representation-theoretic meaning.

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