On Certain Varieties Attached to a Weyl Group Element

  title={On Certain Varieties Attached to a Weyl Group Element},
  author={George Lusztig},
Let B be the variety of Borel subgroups of G. Let W be an indexing set for the set of G-orbits on B × B for the diagonal G-action. Let Ow be the G-orbit corresponding to w ∈ W. Note that W is naturally a Coxeter group with length function l(w) = dimOw − dimB. Let I be an indexing set for the set S of simple reflections of W. Let si ∈ S be the simple reflection corresponding to i ∈ I. For B ∈ B we have gBg−1 ∈ B for any g ∈ D (if q = 1) and F (B) ∈ B (if q > 1). There is a unique automorphism of… CONTINUE READING

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