2018/05/02 by Qi Wang, Wang, Qi
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1805.00598
openalex publication_date 2018/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 2011, Howlett and Nguyen \citer1 introduced the concept of a W-graph ideal EJ in ( W,\leqslantL ) with respect to J (a subset of S), where \leqslant L is the left weak order on W. They proved that one can construct a W-graph from a given W-graph ideal by constructing a Hecke module structure on EJ, where the W-graph was introduced by Kazhdan and Lusztig in \cited1. In this paper, we give the relation between Hecke modules on EJ and general Hecke algebras by considering the relation between Hecke modules on EJ and parabolic Hecke modules. And inspired by Lusztig \citeg3, we show that the parabolic Hecke module is isomorphic to a left ideal of the Hecke algebra. Lastly, we give the relation between R-polynomials on EJ and parabolic R-polynomials as an application of the main results.