An order-reversing duality map for conjugacy classes in Lusztig's canonical quotient
Representation Theory
2007-05-23 v3
Abstract
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.
Keywords
Cite
@article{arxiv.math/0203082,
title = {An order-reversing duality map for conjugacy classes in Lusztig's canonical quotient},
author = {Pramod Achar},
journal= {arXiv preprint arXiv:math/0203082},
year = {2007}
}
Comments
27 pages; corrected attributions of earlier work in the last section