The pop-switch planar algebra and the Jones-Wenzl idempotents.

The Jones-Wenzl idempotents are elements of the Temperley-Lieb (TL) planar algebra that are important, but complicated to write down. We will present a new planar algebra, the pop-switch planar algebra (PSPA), which contains the TL planar algebra. It is motivated by Jones' idea of the graph planar algebra (GPA) of type A_n. In the tensor category of idempotents of the PSPA, the nth Jones-Wenzl idempotent is isomorphic to a direct sum of n + 1 diagrams consisting of only vertical strands. [ABSTRACT FROM AUTHOR]