to follow

to follow

to follow

The sl_3 web category is a combinatorial model for the representation theory of the quantum group U_q(sl_3). We study the category from the cellular point of view, exploiting diagrammatic methods and light-ladder bases to compute branching rules, homomorphisms, and composition factors of cell modules when q is a root of unity. We then apply these results to the study of clasps. In the semisimple case, these higher rank analogues of the Jones—Wenzl idempotents can be constructed using Elias’s recursive triple-clasp expansion. When q is a root of unity, however, their construction is considerably more subtle, and we use the aforementioned results from cellularity to obtain formulas for some of the non-semisimple clasps.

to follow

to follow

to follow

to follow

to follow