A geometric Schur functor

Carl Mautner ^[1]
1. [1] Max Planck Institut für Mathematik
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 20, Nº. 4, 2014, págs. 961-977
Idioma: inglés
DOI: 10.1007/s00029-014-0147-9
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Resumen
- We give geometric descriptions of the category Ck(n,d)Ck(n,d) of rational polynomial representations of GLnGLn over a field kk of degree dd for d≤nd≤n , the Schur functor and Schur–Weyl duality. The descriptions and proofs use a modular version of Springer theory and relationships between the equivariant geometry of the affine Grassmannian and the nilpotent cone for the general linear groups. Motivated by this description, we propose generalizations for an arbitrary connected complex reductive group of the category Ck(n,d)Ck(n,d) and the Schur functor.