On the homology of exotic Springer fibers

Details On the homology of exotic Springer fibers On the homology of exotic Springer fibers

2011-09-20

arxiv.org/abs/1109.4321v1

Mathematics

Representation Theory

36 pages

Scientific paper

We determine the structure of the total homology groups of exotic Springer fibers as affine Weyl group representations. As applications, we provide single top/socle property of standard modules in the exotic Deligne-Langlands correspondence (except for root of unity case), an analogue of Verma's theorem, the coincidence of analytic/geometric gradings in the $C ^{\infty}$-realization of anti-spherical modules of graded Hecke algebras of type $\mathsf{BC}$ with unequal parameters, among others.

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