Web Calculus and Tilting Modules in Type C₂

2020/09/29 by Bodish, Elijah
#FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2009.13786

Abstract

Using Kuperberg's B₂/C₂ 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 \mathfrakso₅≅ \mathfraksp₄ (and the associated quantum group). Our argument has very little dependence on the base field. As a result, we prove that when [2]_q≠ 0, the Karoubi envelope of the C₂ web category is equivalent to the category of tilting modules for the divided powers quantum group U_q^ℤ(\mathfraksp₄).

Related

• Tilting modules and torsion phenomena
• On webs in quantum type C
• Tensor ideals for quantum groups via minimal tilting complexes
• Factorizable sheaves and quantum groups
• Tensor ideals in the category of tilting modules