The Schur functor and its inverses give an important connection between the representation theories of the symmetric group and the general linear group. Kleshchev and Nakano proved in 2001 that when the characteristic of the field is at least 5, the image of the Specht module under the inverse Schur functor is isomorphic to the dual Weyl module. In this talk I will address what happens in characteristics 2 and 3: in characteristic 3, the isomorphism holds, and I will give an elementary proof of this fact which covers also all characteristics other than 2; in characteristic 2, the isomorphism does not hold for all Specht modules, and I will classify those for which it does. Our approach is with Young tableaux, tabloids and Garnir relations.
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- Junior Algebra and Representation Theory Seminar