Webs and tilting modules in type C

Abstract: Using Kuperberg's $B_2/C_2$ webs, and following Elias and Libedinsky, we describe a "light leaves" algorithm to construct a basis of morphisms between arbitrary tensor products of fundamental representations for the Lie algebra of type $C_2$ (and the associated quantum group). Our argument has very little dependence on the base field. As a result, we prove that when quantum two is invertible, the Karoubi envelope of the $C_2$ web category is equivalent to the category of tilting modules for the divided powers quantum group. Time permitting we will also discuss how the “light leaves” basis leads to new formulas for generalized “Jones-Wenzl” projectors in $C_2$ webs, and mention work in progress with Elias, Rose, and Tatham about higher rank type $C$ webs.

commutative algebracombinatoricscategory theoryrepresentation theory

Audience: researchers in the topic

UC Davis algebra & discrete math seminar