2008/10/31 by Jae-Hoon Kwon, Kwon, Jae-Hoon
Mathematics · #17B37 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT) #math.CO #math.RT #msc:17B37
paper · pdf · doi:10.48550/arxiv.0810.5652
arxiv created 2008/10/31 · openalex publication_date 2008/10/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that the Robinson-Schensted-Knuth correspondence is a \gl∞-crystal isomorphism between two realizations of the crystal graph of a generalized Verma module with respect to a maximal parabolic subalgebra of \gl∞. %This extends the previously known result that %the RSK correspondence is an isomorphism of bicrystals or double %crystals. A flagged version of the RSK correspondence is derived in a natural way by computing a Demazure crystal graph of a generalized Verma module. As an application, we discuss a relation between a Demazure crystal and plane partitions with a bounded condition.