2004/07/03 by Tom Roby, Roby, Tom, Itaru Terada +1
Engineering · Mathematics · #05E10 #05E15 #17B20 #20G05 #22E46 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications #Representation Theory (math.RT) #graph theory and CDMA systems #math.CO #math.RT #msc:05E10 #msc:05E15 #msc:17B20 #msc:20G05 #msc:22E46
paper · pdf · doi:10.48550/arxiv.math/0407046
42 pages
arxiv created 2004/07/03 · openalex publication_date 2004/07/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give the first two-dimensional pictorial presentation of Berele's correspondence \citeBerele, an analogue of the Robinson-Schensted (R-S) correspondence \citeRobinson, Schensted for the symplectic group Sp(2n, \Cpx ). From the standpoint of representation theory, the R-S correspondence combinatorially describes the irreducible decomposition of the tensor powers of the natural representation of GL(n,\Cpx). Berele's insertion algorithm gives the bijection that describes the irreducible decomposition of the tensor powers of the natural representation of Sp(2n, \Cpx). Two-dimensional pictorial presentations of the R-S correspondence via local rules (first given by S. Fomin \citeFomin,FominGen) and its many variants have proven very useful in understanding their properties and creating new generalizations. We hope our new presentation will be similarly useful.