10.1016/j.jalgebra.2019.07.027
Brown, Adam
Adam
Brown
Arakawa-Suzuki functors for Whittaker modules
Elsevier
2019
2019-08-22T07:54:13Z
2020-01-16T10:18:55Z
journal_article
/record/6828
/record/6828.json
0021-8693
1805.04676
In this paper we construct a family of exact functors from the category of Whittaker modules of the simple complex Lie algebra of type to the category of finite-dimensional modules of the graded affine Hecke algebra of type . Using results of Backelin [2] and of Arakawa-Suzuki [1], we prove that these functors map standard modules to standard modules (or zero) and simple modules to simple modules (or zero). Moreover, we show that each simple module of the graded affine Hecke algebra appears as the image of a simple Whittaker module. Since the Whittaker category contains the BGG category as a full subcategory, our results generalize results of Arakawa-Suzuki [1], which in turn generalize Schur-Weyl duality between finite-dimensional representations of and representations of the symmetric group .