Abstract
In this article, we compute the center of the infinitesimal Hecke algebras H z associated to ๐ฐ๐ฉ2; then using nontriviality of the center, we study representations of these algebras in the framework of the BGG category ๐ช. We also discuss central elements in infinitesimal Hecke algebras over ๐ค๐ฉ n and ๐ฐ๐ญ(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.