Pith. sign in

REVIEW 3 cited by

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1409.2799 v2 pith:CPZKFGQP submitted 2014-09-09 math.QA math.GTmath.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
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
0 comments
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.

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.