ON CHARACTER SHEAVES AND CHARACTERS OF REDUCTIVE GROUPS AT UNIPOTENT CLASSESReport as inadecuate




ON CHARACTER SHEAVES AND CHARACTERS OF REDUCTIVE GROUPS AT UNIPOTENT CLASSES - Download this document for free, or read online. Document in PDF available to download.

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée 2 School of Mathematics and statistics Sydney 3 IMJ - Institut de Mathématiques de Jussieu

Abstract : With a view to determining character values of finite reductive groups at unipotent elements, we prove a number of results concerning inner products of generalised Gelfand-Graev characters with characteristic functions of character sheaves, here called Lusztig functions. These are used to determine projections of generalised Gelfand-Graev characters to the space of unipotent characters, and to the space of characters with a given wave front set. Such projections are expressed largely in terms of Weyl group data. We show how the values of characters at their unipotent support or wave front set are determined by such data. In some exceptional groups we show that the projection of a generalised Gelfand-Graev character to a family with the same wave front set is up to sign the dual of a Mellin transform. Using these results, in certain cases we are able to determine roots of unity which relate almost characters to the characteristic functions. In particular we show how to compute the values of all unipotent characters at all unipotent classes for the exceptional adjoint groups of type G2 , F4 , E6 , E7 and E8 . We also provide an appendix which gives a complete list of the cuspidal character sheaves on all quasi-simple groups.

Keywords : reductive group character sheaf Gelfand-Graev





Author: François Digne - Gus Lehrer - Jean Michel -

Source: https://hal.archives-ouvertes.fr/



DOWNLOAD PDF




Related documents