Journal article
Springer correspondence for the split symmetric pair in type A
TH Chen, K Vilonen, T Xue
Compositio Mathematica | CAMBRIDGE UNIV PRESS | Published : 2018
Abstract
In this paper we establish Springer correspondence for the symmetric pair using Fourier transform, parabolic induction functor, and a nearby cycle sheaf construction. As an application of our results we see that the cohomology of Hessenberg varieties can be expressed in terms of irreducible representations of Hecke algebras of symmetric groups at . Conversely, we see that the irreducible representations of Hecke algebras of symmetric groups at arise in geometry.
Grants
Awarded by University of Chicago
Funding Acknowledgements
We thank Misha Grinberg for helpful conversations. T.C. thanks Cheng-Chiang Tsai for useful discussions and thanks the Institute of Mathematics Academia Sinica in Taipei for support, hospitality, and a nice research environment. T.X. thanks Syu Kato for helpful discussions. Furthermore, K.V. and T.X. thank the Research Institute for Mathematical Sciences in Kyoto for support, hospitality, and a nice research environment. We also would like to thank the referee for carefully reading our manuscript and for helpful comments.