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The discovery of the Jones polynomial triggered mathematical developments in areas including knot theory and quantum algebra. One way to define the Jones polynomial is by using the braiding in the Temperley-Lieb category. The representation category of quantum sl_2 can be "visualized" by looking at the planar graphs in the Temperley-Lieb category, and an interesting question is how to describe the irreducible representations of quantum sl_2 with these planar graphs. An answer to this question is called the Jones-Wenzl projectors. With Kuperberg's Spiders for rank two Lie algebras, we can ask the same question for the rank two cases, including g_2. This talk is based on joint work with Elijah Bodish from University of Oregon.(arxiv:2112.01007)