Abstract
In this article, we compute the center of the infinitesimal Hecke algebras H z associated to š¯”°š¯”©2; then using nontriviality of the center, we study representations of these algebras in the framework of the BGG category š¯’Ŗ. We also discuss central elements in infinitesimal Hecke algebras over š¯”¤š¯”© n and š¯”°š¯”(2n) for all n. We end by proving an analogue of Duflo's theorem for H z .
2000 Mathematics Subject Classification:
ACKNOWLEDGMENTS
We thank the referee for his patient reading, and for making numerous suggestions and comments, which helped in improving this manuscript.
This article is essentially an improved write-up of A.T.'s Ph.D. thesis from the University of Chicago, and Section 2 is a more detailed exposition of an earlier preprint [Citation10].
Notes
Communicated by K. Misra.