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Green Functions Associated to Complex Reflection Groups

✍ Scribed by Toshiaki Shoji

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
314 KB
Volume
245
Category
Article
ISSN
0021-8693

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✦ Synopsis

Green functions of classical groups are determined by the data from Weyl groups and by certain combinatorial objects called symbols. Generalizing this, we Ž . define Green functions associated to complex reflection groups G e, 1, n and study their combinatorial properties. We construct Hall᎐Littlewood functions and Schur functions in our scheme and show that such Green functions are obtained as a transition matrix between those two symmetric functions, as in the case of GL . n ᮊ 2001 Academic Press CONTENTS 0. Introduction. 1. Preliminaries. 2. Symmetric functions associated to partitions. 3. Symmetric functions associated to symbols. 4. Hall᎐Littlewood functions. 5. Green functions. 6. Some special cases. 7. Examples.

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