Representations of Temperley--Lieb Algebras

الأصل · EN

We define a commuting family of operators T₀,T₁,...,Tₙ in the Temperley--Lieb algebra Aₙ(x) of type Aₙ₋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 Aₙ(x). These results are used to provide the Temperley--Lieb algebras of type Aₙ₋₁ with a semi--normal form, together with a branching law, and explicit formulae for associated Gram determinants.