Lusztig's canonical quotient and generalized duality

Authors

E Sommers, University of Massachusetts - AmherstFollow

Publication Date

2001

Journal or Book Title

JOURNAL OF ALGEBRA

Abstract

We give a new characterization of Lusztig's canonical quotient, a finite group attached to each special nilpotent orbit of a complex semisimple Lie algebra. This group plays an important role in the classification of unipotent representations of finite groups of Lie type. We also define a duality map. To each pair of a nilpotent orbit and a conjugacy class in its fundamental group, the map assigns a nilpotent orbit in the Langlands dual Lie algebra. This map is surjective and is related to a map introduced by Lusztig (and studied by Spaltenstein). When the conjugacy class is trivial, our duality map is just the one studied by Spaltenstein and by Barbasch and Vogan which has an image of the set of special nilpotent orbits.

Comments

The published version is located at http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WH2-4582D7K-37&_user=1516330&_coverDate=09%2F15%2F2001&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1662344449&_rerunOrigin=google&_acct=C000053443&_version=1&_urlVersion=0&_userid=1516330&md5=ce5ef4b7fd194f2192919cffec556937&searchtype=a

Pages

790-812

Volume

243

Issue

2

Recommended Citation

Sommers, E, "Lusztig's canonical quotient and generalized duality" (2001). JOURNAL OF ALGEBRA. 791.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/791