The partial Temperley-Lieb algebra and its representations

DOI10.4171/jca/74zbMath1527.05174arXiv2208.04296MaRDI QIDQ6060952

Anthony Giaquinto, Stephen R. Doty

Publication date: 30 November 2023

Published in: Journal of Combinatorial Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2208.04296

zbMATH Keywords

Temperley-Lieb algebrasSchur-Weyl dualityquantized enveloping algebrasdiagram algebras

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Quantum groups (quantized enveloping algebras) and related deformations (17B37) Representations of orders, lattices, algebras over commutative rings (16G30) Representation theory of associative rings and algebras (16G99) Connections of Hopf algebras with combinatorics (16T30)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Motzkin monoids and partial Brauer monoids
• Partition algebras.
• State models and the Jones polynomial
• Hecke algebra representations of braid groups and link polynomials
• Quantum Weyl reciprocity and tilting modules
• Iterated inflations of cellular algebras
• Index for subfactors
• The representation theory of the Temperley-Lieb algebras
• Cellular algebras
• Standard modules, induction and the structure of the Temperley-Lieb algebra
• Partition algebras and the invariant theory of the symmetric group
• Motzkin algebras
• A characteristic free approach to Brauer algebras
• ON THE REPRESENTATION THEORY OF PARTIAL BRAUER ALGEBRAS
• Partition algebras Pk(n) with 2k>n and the fundamental theorems of invariant theory for the symmetric group Sn
• ENDOMORPHISMS OF , , AND
• A polynomial invariant for knots via von Neumann algebras
• Cellular Algebras: Inflations and Morita Equivalences
• Presenting generalized 𝑞-Schur algebras
• Braids, Link Polynomials and a New Algebra
• Representations of the Rook-Brauer Algebra
• Relations between the ‘percolation’ and ‘colouring’ problem and other graph-theoretical problems associated with regular planar lattices: some exact results for the ‘percolation’ problem
• Introduction to quantum groups