2014/08/31 by Naihuan Jing, Yunnan Li · 17 citations
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebra over a field #Algebraic structures and combinatorial models #Basis (linear algebra) #Combinatorics #Computer science #Geometry #Lift (data mining) #Macdonald polynomials #Mathematics #Noncommutative geometry #Orthogonal polynomials #Pure mathematics #Schur algebra #Schur polynomial #Schur's theorem #Simple (philosophy) #math.CO #math.QA #msc:05A99 #msc:05E05 #msc:05E99 #msc:16S99 #msc:16T99
paper · pdf · doi:10.1016/j.jcta.2015.05.006
published in Journal of Combinatorial Theory Series A 135, 268-290 (Elsevier BV) · 22 pages, 20refs
arxiv created 2015/01/29 · openalex publication_date 2015/06/12 · arxiv updated 2020/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We construct a lift of Schur's Q-functions to the peak algebra of the symmetric group, called the noncommutative Schur Q-functions, and extract from them a new natural basis with several nice properties such as the positive right-Pieri rule, combinatorial expansion, etc. Dually, we get a basis of the Stembridge algebra of peak functions refining Schur's P-functions in a simple way.