Abstract
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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Presented by Jon F. Carlson.
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Enyang, J., Goodman, F.M. Cellular Bases for Algebras with a Jones Basic Construction. Algebr Represent Theor 20, 71–121 (2017). https://doi.org/10.1007/s10468-016-9632-5
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DOI: https://doi.org/10.1007/s10468-016-9632-5
Keywords
- Cellular algebra
- Jones basic construction
- Murphy basis
- Brauer algebra
- Birman–Murakami–Wenzl algebra
- Partition algebra