Exotic Springer fibers for orbits corresponding to one-row bipartitions

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.

27 pages, minor revisions, two-boundary diagrammatics changed to one-boundary diagrammatics, to appear in Transform. Groups

References in corpus (9)

• The two-boundary Temperley-Lieb algebra
• Annular Khovanov homology and knotted Schur-Weyl representations
• A remark on the topology of (n,n) Springer varieties
• Schur-Weyl duality, Verma modules, and row quotients of Ariki-Koike algebras
• Two boundary Hecke Algebras and combinatorics of type C
• Irreducible components of two-row Springer fibers and Nakajima quiver varieties
• Irreducible components of exotic Springer fibres
• Irreducible Components of Exotic Springer fibres II: The Exotic Robinson-Schensted Algorithm
• Quantum Schur duality of affine type C with three parameters