Justin Lambright ; Mark Skandera - Combinatorial formulas for double parabolic R-polynomials

dmtcs:2825 - Discrete Mathematics & Theoretical Computer Science, January 1, 2010, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) - https://doi.org/10.46298/dmtcs.2825
Combinatorial formulas for double parabolic R-polynomialsArticle

Authors: Justin Lambright 1; Mark Skandera 2

  • 1 Lehigh University [Bethlehem]
  • 2 Department of Mathematics

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.


Volume: DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)
Section: Proceedings
Published on: January 1, 2010
Imported on: January 31, 2017
Keywords: Immanants,Kazhdan-Lusztig polynomials,quantum groups,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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