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Springer correspondence for the split symmetric pair in type $A

Compositio mathematica, 2018-11, Vol.154 (11), p.2403-2425, Article 2403 [Peer Reviewed Journal]

The Authors 2018 ;ISSN: 0010-437X ;EISSN: 1570-5846 ;DOI: 10.1112/S0010437X18007443

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  • Title:
    Springer correspondence for the split symmetric pair in type $A
  • Author: Chen, Tsao-Hsien ; Vilonen, Kari ; Xue, Ting
  • Subjects: Fourier transforms ; Grants ; Group theory ; Homology ; Orbits ; Representations
  • Is Part Of: Compositio mathematica, 2018-11, Vol.154 (11), p.2403-2425, Article 2403
  • Description: In this paper we establish Springer correspondence for the symmetric pair $(\text{SL}(N),\text{SO}(N))$ 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 $q=-1$ . Conversely, we see that the irreducible representations of Hecke algebras of symmetric groups at $q=-1$ arise in geometry.
  • Publisher: London, UK: London Mathematical Society
  • Language: English;French
  • Identifier: ISSN: 0010-437X
    EISSN: 1570-5846
    DOI: 10.1112/S0010437X18007443
  • Source: AUTh Library subscriptions: ProQuest Central
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