Parabolic generalization of Kazhdan-Lusztig polynomials and bases (Q1283658)

For a Coxeter system and a parabolic subsystem, one considers the two corresponding Hecke algebras. Each linear character of the parabolic Hecke algebra gives rise to two families of Kazhdan-Lusztig polynomials, for which the author computes the classical properties: existence and uniqueness, symmetry, duality, induction formulas, and computation of the polynomials using distinguished subexpressions of a Coxeter group element. This generalizes Deodhar's construction, which corresponds to the extreme case of sign and index characters. Finally, the author gives formulas for the action of the Hecke algebra on the induced modules in terms of Kazhdan-Lusztig bases.