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arXiv · 2009.13786

Web Calculus and Tilting Modules in Type $C_2$

Elijah Bodish
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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 $\mathfrak{so}_5\cong \mathfrak{sp}_4$ (and the associated quantum group). Our argument has very little dependence on the base field. As a result, we prove that when $[2]_q\ne 0$, the Karoubi envelope of the $C_2$ web category is equivalent to the category of tilting modules for the divided powers quantum group $\mathcal{U}_q^{\mathbb{Z}}(\mathfrak{sp}_4)$.

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Elijah Bodish. 2020-09-29. Web Calculus and Tilting Modules in Type $C_2$. https://arxiv.org/abs/2009.13786

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