Abstract
We extend previous work by constructing a universal abelian tensor category Tt generated by two objects X, Y equipped with finite filtrations 0⊊X0⊊...⊊Xt+1=X and 0⊊Y0⊊...⊊Yt+1=Y, and with a pairing X⊗Y→1, where 1 is the monoidal unit. This category is modeled as a category of representations of a Mackey Lie algebra glM(V,V∗) of cardinality 2ℵt, associated to a diagonalizable pairing between two vector spaces V,V∗ of dimension ℵt over an algebraically closed field K of characteristic 0. As a preliminary step, we study a tensor category Tt generated by the algebraic duals V∗ and (V∗)∗. The injective hull of the trivial module K in Tt is a commutative algebra I, and the category Tt consists of all free I-modules in Tt. An essential novelty in our work is the explicit computation of Ext-spaces between simples in both categories Tt and Tt, which had been an open problem already for t=0. This provides a direct link from the theory of universal tensor categories to Littlewood-Richardson-type combinatorics.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callSimilar Papers
More From: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
