Séance Séminaire

Séminaire Algèbre Géométrie Algébrique Topologie Algébrique

Hochschild cohomology and graded Hecke algebras

A graded Hecke algebra is an associative algebra defined by Drinfeld in terms of a finite group $G$ and a finite dimensional representation $V$. These algebras have been studied for particular types of groups by many people including Lusztig (real reflection groups), Ram-Shepler (complex reflection groups), and Etingof-Ginzburg (symplectic reflection groups). A graded Hecke algebra is formally a particular type of deformation of the skew group algebra of the symmetric algebra $S(V)$ and the group $G$. This is the point of view we will take in our talk, making a direct connection with Hochschild cohomology, as well as giving new examples.