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We study two families of polynomials that play the same role, in thegeneralized Temperley Lieb algebra of a Coxeter group, as the Kazhdan Lusztigand R polynomials in the Hecke algebra of the group. Our results includerecursions, closed formulas, and other combinatorial properties for thesepolynomials. We focus mainly on non branching Coxeter graphs.

Kazhdan Lusztig and R polynomials of generalized Temperley Lieb algebras