2024/07/29 by Thibault D. Décoppet, Décoppet, Thibault D. · 2 citations
Mathematics · #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #Advanced Algebra and Geometry
paper · pdf · doi:10.48550/arxiv.2407.20211
Over a field of characteristic p>0, the higher Verlinde categories Verpn are obtained by taking the abelian envelope of quotients of the category of tilting modules for the algebraic group SL2. These symmetric tensor categories have been introduced in arXiv:2003.10499 & arXiv:2003.10105, and their properties have been extensively studied in the former reference. In arXiv:2105.07724, the above construction for SL2 has been generalized to Lusztig's quantum group for \mathfraksl2 and root of unity ζ, which produces the mixed higher Verlinde categories Verζp(n). Inspired by the results of arXiv:2003.10499, we study the properties of these braided tensor categories in detail. In particular, we establish a Steinberg tensor product formula for the simple objects of Verζp(n), construct a braided embedding Verpn\hookrightarrow Verζp(n+1), compute the symmetric center of Verζp(n), and identify its Grothendieck ring.