On the topology of components of some Springer fibers and their relation to Kazhdan-Lusztig theory

Details On the topology of components of some Springer fibers and their relation to Kazhdan-Lusztig theory On the topology of components of some Springer fibers and their relation to Kazhdan-Lusztig theory

2002-04-18

arxiv.org/abs/math/0204224v1

Mathematics

Representation Theory

This work has been submitted to Advances in Mathematics (Academic Press) for possible publication.

Scientific paper

We describe the irreducible components of Springer fibers for hook and two-row nilpotent elements of gl_n(C) as iterated bundles of flag manifolds and Grassmannians. We then relate the topology (in particular, the intersection homology Poincare' polynomials) of the intersections of these components with the inner products of the Kazhdan-Lusztig basis elements of irreducible representations of the rational Iwahori-Hecke algebra of type A corresponding to the hook and two-row Young shapes.

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