City Research Online

Abstract

We study the geometry and topology of exotic Springer fibers for orbits corresponding to one-row bipartitions from an explicit, combinatorial point of view. This includes a detailed analysis of the structure of the irreducible components and their intersections as well as the construction of an explicit affine paving. Moreover, we compute the ring structure of cohomology by constructing a CW-complex homotopy equivalent to the exotic Springer fiber. This homotopy equivalent space admits an action of the type C Weyl group inducing Kato’s original exotic Springer representation on cohomology. Our results are described in terms of the diagrammatics of the one-boundary Temperley–Lieb algebra (also known as the blob algebra). This provides a first step in generalizing the geometric versions of Khovanov’s arc algebra to the exotic setting.

Publication Type:	Article
Additional Information:	This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s00031-020-09613-0
Subjects:	Q Science > QA Mathematics Q Science > QC Physics T Technology > TA Engineering (General). Civil engineering (General)
Departments:	School of Science & Technology School of Science & Technology > Mathematics
SWORD Depositor:	Symplectic Administrator

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