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Exotic Springer fibers for orbits corresponding to one-row bipartitions

Exotic Springer fibers for orbits corresponding to one-row bipartitions

Saunders, Neil and Wilbert, Arik (2020) Exotic Springer fibers for orbits corresponding to one-row bipartitions. [Working Paper] (In Press)

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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.

Item Type: Working Paper
Uncontrolled Keywords: Springer Fibres, Diagram Algebra, Khovanov Homology
Subjects: Q Science > QA Mathematics
Faculty / Department / Research Group: Faculty of Liberal Arts & Sciences
Faculty of Liberal Arts & Sciences > School of Computing & Mathematical Sciences (CAM)
Last Modified: 26 Nov 2020 23:01
Selected for GREAT 2016: None
Selected for GREAT 2017: None
Selected for GREAT 2018: None
Selected for GREAT 2019: None
Selected for REF2021: REF 1
URI: http://gala.gre.ac.uk/id/eprint/28293

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