2014/12/01 by Olga Azenhas, Azenhas, Olga, Aram Emami +1
Mathematics · Physics and Astronomy · #17B37 #Advanced Algebra and Geometry #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #Nonlinear Waves and Solitons #Primary 05E05. Secondary 05E10 #Representation Theory (math.RT) #math.CO #math.RT #msc:05E05. #msc:05E10 #msc:17B37
paper · pdf · doi:10.48550/arxiv.1412.0420
Extended abstract, 17 pages
arxiv created 2014/12/01 · openalex publication_date 2014/12/01 · arxiv updated 2014/12/02 · openalex created_date 2016/08/23 · openalex updated_date 2026/07/28
Lascoux has given a triangular version of the Cauchy identity where Schur polynomials are replaced by Demazure characters and Demazure atoms. He has then used the staircase expansion to recover expansions for all Ferrers shapes, where the Demazure characters and Demazure atoms are under the action of Demazure operators specified by the cells above the staircase. The characterisation of the tableau-pairs in these last expansions is less explicit. We give here a bijective proof for expansions over near staircases, where the tableau-pairs are made explicit. Our analysis formulates Mason's RSK analogue, for semi-skylines augmented fillings, in terms of growth diagrams.