2012/09/12 by Hiraku Abe, Abe, Hiraku, Tomoo Matsumura +1 · 1 citation
Mathematics · #05E05 (Primary) #05E15 #57R18 (Secondary) #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #math.AT #math.CO #msc:05E05 #msc:05E15 #msc:57R18
paper · pdf · doi:10.48550/arxiv.1209.2597
13 pages. Comments are welcome
openalex publication_date 2012/09/12 · arxiv created 2015/01/30 · arxiv updated 2015/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we introduce a family of symmetric polynomials by specializing the factorial Schur polynomials. These polynomials represent the weighted Schubert classes of the cohomology of the weighted Grassmannian introduced by Corti-Reid, and we regard these polynomials as analogue of the Schur polynomials. We show that those twisted Schur polynomials are the characters of certain representations. Thus we give an interpretation of the Schubert structure constants of the weighted Grassmannians as the (rational) multiplicities of tensor products of the representations. Furthermore, we derive two types of determinantal formulas for the weighted Schubert classes, in terms of special weighted Schubert classes, and also in terms of Chern classes of tautological orbi-bundles.