Diagrammatic morphisms between indecomposable modules of Ūq(𝔰𝔩2)

@article{Moore2018DiagrammaticMB,
  title={Diagrammatic morphisms between indecomposable modules of Ūq(𝔰𝔩2)},
  author={Stephen T. Moore},
  journal={International Journal of Mathematics},
  year={2018},
  volume={31},
  pages={2050016}
}
  • Stephen T. Moore
  • Published 5 November 2018
  • Mathematics
  • International Journal of Mathematics
We give diagrammatic formulae for morphisms between indecomposable representations of Ūq(𝔰𝔩2) appearing in the decomposition of (ℂ2)⊗n, including projections and second endomorphisms on projective ... 
View PDF on arXiv
3 Citations
Results Citations
1

3 Citations

DIAGRAMMATIC CONSTRUCTION OF REPRESENTATIONS OF SMALL QUANTUM sl 2

. We provide a combinatorial description of the monoidal category generated by the fundamental representation of the small quantum group of sl 2 at a root of unity q of odd order. Our approach is…

Limits of traces of Temperley-Lieb algebras

We review the classification of positive extremal traces on the generic infinite Temperley-Lieb algebra, and then extend the classification to the non-semisimple root of unity case. As a result, we…

Non-semisimple 3-manifold invariants derived from the Kauffman bracket

We recover the family of non-semisimple quantum invariants of closed oriented 3-manifolds associated with the small quantum group of $\mathfrak{sl}_2$ using purely combinatorial methods based on…

References

SHOWING 1-10 OF 32 REFERENCES

Non-semisimple planar algebras from Ūq(sl2)

We construct examples of non-semisimple tensor categories using planar algebras, with our main focus being on a construction from the restricted quantum group Ūq(sl_2). We describe the generators and…

Non-semisimple planar algebras from the representation theory of Ūq(𝔰𝔩2)

We describe the generators and prove a number of relations for the construction of a planar algebra from the restricted quantum group [Formula: see text]. This is a diagrammatic description of…

Indecomposable decomposition of tensor products of modules over the restricted quantum universal enveloping algebra associated to sl2

A CONSTRUCTION OF SYMMETRIC LINEAR FUNCTIONS ON THE RESTRICTED QUANTUM GROUP Uq(sl 2)

In this article we construct all the primitive idempotents o f the restricted quantum group Uq (sl2) and also describe Uq (sl2) as the subalgebra of the direct sum of matrix algebras. By using this…

Finite Dimensional Representations of Ut (sl (2)) at Roots of Unity

  • X. Jie
  • Mathematics
    Canadian Journal of Mathematics
  • 1997
Abstract All finite dimensional indecomposable representations of Ut (Sl (2)) at roots of 1 are determined.

ON SCHUR-WEYL DUALITY, An HECKE ALGEBRAS AND QUANTUM sl(N) ON $\otimes^{n+1}{\mathbb C}^N$

We prove that an N-state vertex model representation of the An Hecke algebra quotient NHn(q) is faithful for all q. We use the result to examine the indecomposable content of these representations,…

Skein theory for the D_2pi planar algebras

Evaluable Jones-Wenzl idempotents at root of unity and modular representation on the center of U_qsl(2)

Let p an integer. We define a family of idempotents (and nilpotents) in the Temperley - Lieb algebras at 4p-th roots of unity which generalize the usual Jones-Wenzl idempotents. These new idempotents…

Modular Group Representations and Fusion in Logarithmic Conformal Field Theories and in the Quantum Group Center

The SL(2, ℤ)-representation π on the center of the restricted quantum group at the primitive 2pth root of unity is shown to be equivalent to the SL(2, ℤ)-representation on the extended characters of…

SCHUR-WEYL DUALITY

Introduction 1 1. Representation Theory of Finite Groups 2 1.1. Preliminaries 2 1.2. Group Algebra 4 1.3. Character Theory 5 2. Irreducible Representations of the Symmetric Group 8 2.1. Specht…