An exotic Springer correspondence for symplectic groups

Details An exotic Springer correspondence for symplectic groups An exotic Springer correspondence for symplectic groups

2006-07-19

arxiv.org/abs/math/0607478v2

Mathematics

Representation Theory

v2; 16pp. title changed, Nov/07 version except for one reference, may be merged into next revision of math.RT/0601155

Scientific paper

This paper is a sequel to math.RT/0601155. Let G be a complex symplectic group. In math.RT/0601155, we constructed a certain G-variety N = N_1, which we call the (1-) exotic nilpotent cone. In this paper, we study the set of G-orbits of the variety N. It turns out that the variety N gives a variant of the Springer correspondence for the Weyl group of type C, but shares a similar flavor with that of type A case. (I.e. there appears no non-trivial local system and the correspondence is bijective.) As an application, we present one sufficient condition for the bijectivity of our exotic Deligne-Langlands correspondence [K1].

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