Mathematics Colloquia and Seminars

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The well-known Robinson-Schensted correspondence gives a concrete combinatorial realization of the irreducible decomposition of the natural representation of the group $GL(n,\C)$ on $(\C^n)^{\otimes f}$. Berele's correspondence is an analogue of the Robinson-Schensted correspondence for the symplectic group Sp(2n, C), describing the irreducible decomposition of the tensor powers of the natural representation of Sp( 2n, C). Two-dimensional pictorial presentations of the R-S correspondence and its many variants via local rules (first given by S.Fomin) have proven very useful in understanding properties of these algorithms and creating new generalizations. We will describe these local rules for the R-S correspondence and give the first two-dimensional pictorial presentation of Berele's correspondence. This is joint work with Itaru Terada (Tokyo).