pith. sign in

arxiv: 1409.2799 · v2 · pith:CPZKFGQPnew · submitted 2014-09-09 · 🧮 math.QA · math.GT· math.RT

Diagram categories for U_q-tilting modules at roots of unity

Henning Haahr Andersen , Daniel Tubbenhauer This is my paper
classification 🧮 math.QA math.GTmath.RT
keywords mathfrakgiveunitycategorydiagrammaticgradingmodulesroot
0
0 comments X
read the original abstract

We give a diagrammatic presentation of the category of $\textbf{U}_q(\mathfrak{sl}_2)$-tilting modules $\mathfrak{T}$ for $q$ being a root of unity and introduce a grading on $\mathfrak{T}$. This grading is a "root of unity phenomenon" and might lead to new insights about link and $3$-manifold invariants deduced from $\mathfrak{T}$. We also give a diagrammatic category for the (graded) projective endofunctors on $\mathfrak{T}$, indicate how our results could generalize and collect some "well-known" facts to give a reasonably self-contained exposition.

This paper has not been read by Pith yet.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. On a symplectic quantum Howe duality

    math.RT 2023-03 unverdicted novelty 7.0

    Proves nonsemisimple quantum Howe duality for Sp(2n) and SL(2) on exterior algebra of type C, with character formulas and canonical bases.

  2. On Hecke and asymptotic categories for a family of complex reflection groups

    math.RT 2024-09 unverdicted novelty 6.0

    Constructs Hecke algebras and asymptotic versions for G(M,M,N) complex reflection groups by generalizing the dihedral case.

  3. Orthogonal webs and semisimplification

    math.RT 2024-01 unverdicted novelty 4.0

    A diagrammatic category equivalent to tilting representations of the orthogonal group is defined and its semisimplification is described, valid in characteristic not equal to two.