Representations of Temperley--Lieb Algebras

Details Representations of Temperley--Lieb Algebras Representations of Temperley--Lieb Algebras

2007-10-17

arxiv.org/abs/0710.3218v1

Mathematics

Representation Theory

23 pages, 1 figure

Scientific paper

We define a commuting family of operators $T_0,T_1,...,T_n$ in the Temperley--Lieb algebra $\mathcal{A}_n(x)$ of type $A_{n-1}$. Using an appropriate analogue to Murphy basis of the Iwahori--Hecke algebra of the symmetric group, we describe the eigenvalues arising from the triangular action of the said operators on the cell modules of $\mathcal{A}_n(x)$. These results are used to provide the Temperley--Lieb algebras of type $A_{n-1}$ with a semi--normal form, together with a branching law, and explicit formulae for associated Gram determinants.

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