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Abstract: Let G be a connected reductive algebraic group. Let us consider a product X of flag varieties and the diagonal action of G, which extends to a Hamiltonian action on the cotangent bundle T*X.  Hence we get a moment map. Steinberg considered a conormal variety and deduced a map from the Weyl group W of G to the nilpotent coadjoint orbit in the Lie algebra. In type A, this explains the RS correspondence in the language of geometry. We generalize his theory in type A, and get a bijection between partial permutations and triplets of (pairs of standard tableaux, partition). This generalization involves interesting combinatorics and gives an insight to the representation theory. The talk is based on the on-going joint work with Lucas Fresse at IECL (France).

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