Purity of equivalued affine Springer fibers
By Mark Goresky, R. Kottwitz, Robert D. MacPherson. 2003
77 citations recorded by the source corpus.
The affine Springer fiber corresponding to a regular integral equivalued semisimple element admits a paving by vector bundles over Hessenberg varieties and hence its (Borel-Moore) homology is "pure".
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/dfa37727b200960c101739355639e29eeb477b11
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In Discrete Mathematics and Combinatorics
- Tatsuyuki Hikita
- Alexei Oblomkov
- Julianna Tymoczko
- E. Sommers
- Zhiwei Yun
- Megumi Harada
- Martha Precup
- Paul Blain Levy
In Geometry and Topology
- Alexei Oblomkov
- Julianna Tymoczko
- Tatsuyuki Hikita
- E. Sommers
- Zhiwei Yun
- E. Gorsky
- Jacob Rasmussen
- Vivek V. Shende
In Mathematical Physics
- Alexei Oblomkov
- Julianna Tymoczko
- Tatsuyuki Hikita
- E. Sommers
- Zhiwei Yun
- E. Gorsky
- Tasho Kaletha
- Tom H. Koornwinder
Citations in the corpus
- Affine Springer fibers of type A and combinatorics of diagonal coinvariants (2012, background): “This is the construction of Springer representations due to Lusztig, Borho and MacPherson.”
- Exponents for B-stable ideals (2004, methodology): “Other Hessenberg varieties have been used in [ GKM ] to give a partial proof of the fundamental lemma of the Langlands program.”
- Geometric representations of graded and rational Cherednik algebras (2014, background): “In [21], when e = 1, it is shown that for a class of elements γ ∈ grs(F ) called equivalued, the corresponding affine Springer fiber admits a paving by affine space bundles over Hessenberg varieties that are smooth and projective, and in particular they have pure cohomology.”
- Le lemme fondamental pour les algebres de Lie (2008, unknown): “Cette conjecture a été vérifiée pour les éléments ayant des valuations radicielles égales dans [27].”