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Combinatorial formulas for double parabolic R-polynomials

Abstract : The well-known R-polynomials in ℤ[q], which appear in Hecke algebra computations, are closely related to certain modified R-polynomials in ℕ[q] whose coefficients have simple combinatorial interpretations. We generalize this second family of polynomials, providing combinatorial interpretations for expressions arising in a much broader class of computations. In particular, we extend results of Brenti, Deodhar, and Dyer to new settings which include parabolic Hecke algebra modules and the quantum polynomial ring.
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Justin Lambright, Mark Skandera. Combinatorial formulas for double parabolic R-polynomials. 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), 2010, San Francisco, United States. pp.857-868. ⟨hal-01186253⟩

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