An order-reversing duality map for conjugacy classes in Lusztig's canonical quotient

Details An order-reversing duality map for conjugacy classes in Lusztig's canonical quotient An order-reversing duality map for conjugacy classes in Lusztig's canonical quotient

2002-03-08

arxiv.org/abs/math/0203082v3

Mathematics

Representation Theory

27 pages; corrected attributions of earlier work in the last section

Scientific paper

We define a partial order on the set of pairs {(O,C)}, where O is a nilpotent orbit and C is a conjugacy class in Lusztig's canonical quotient of A(O). We then show that there is a unique order-reversing duality map on this set that has certain properties analagous to those of the original Lusztig-Spaltenstein duality map. This generalizes work of E. Sommers. In this revised version, a new approach leads to a strengthened version of Theorem 2, and applications of the results are discussed in greater detail.

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