Saunders, Neil and Wilbert, Arik (2022) Exotic springer fibers for orbits corresponding to one-row bipartitions. Transformation Groups, 27. pp. 1111-1147. ISSN 1083-4362 (Print), 1531-586X (Online) (doi:10.1007/s00031-020-09613-0)

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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:	Article
Uncontrolled Keywords:	springer fibres; diagram algebra; Khovanov homology
Subjects:	Q Science > QA Mathematics
Faculty / School / Research Centre / Research Group:	Faculty of Engineering & Science Faculty of Engineering & Science > School of Computing & Mathematical Sciences (CMS)
Last Modified:	19 Jan 2024 10:28
URI:	http://gala.gre.ac.uk/id/eprint/28293

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