Cellular Bases for Algebras with a Jones Basic Construction

  title={Cellular Bases for Algebras with a Jones Basic Construction},
  author={John Enyang and Frederick M. Goodman},
  journal={Algebras and Representation Theory},
  • John Enyang, Frederick M. Goodman
  • Published 2011
  • Mathematics
  • We construct analogues for the Brauer, BMW, partition, and Jones–Temperley–Lieb algebras of the Murphy basis of the Hecke algebra of the symmetric group. The bases are cellular bases indexed by paths on branching diagrams, and compatible with restriction of cell modules. The Jucys–Murphy elements for each class of algebras act by triangular matrices on the Murphy basis. 

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