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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.
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This content will become publicly available on January 1, 2026
Totally Symmetric Sets
We survey the theory of totally symmetric sets, with applications to homo- morphisms of symmetric groups, braid groups, linear groups, and mapping class groups.
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- Award ID(s):
- 2417920
- PAR ID:
- 10625136
- Publisher / Repository:
- American Mathematical Society
- Date Published:
- ISSN:
- 0271-4132
- ISBN:
- 9781470475345
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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