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General Jones-Wenzl Idempotents

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The Jones-Wenzl idempotents are celebrated elements of Temperley-Lieb algebras. Their existence have far-reaching consequences and they are the smallest and easiest examples of “clasps” (also known as “magic weave elements”) which arise in the study of certain categories of U_q(sl_n) modules. In this talk, we will take a whirlwind tour through the representation theory of Temperley-Lieb algebras over arbitrary (mixed) characteristic followed by a more sedate, careful, walk through the construction of the generalised Jones-Wenzl idempotents. The procedure is suggestive of a larger theory, and we will briefly touch on applications of the construction to tilting categories and relations to other interesting (positive characteristic) constructions.

This talk is part of the Algebra and Representation Theory Seminar series.

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