Professor Matt Douglass invites you to attend the PhD dissertation defense of Angela Berardinelli in two weeks on Friday, April 24th at 9:00 am in GAB 438. Cake and coffee will be served in GAB 472 following this event.

"Restricting Invariants and Arrangements of Finite Complex Reflection Groups"

Abstract:

Suppose that G is a finite, unitary reflection group acting on a complex vector space V and X is a subspace of V. Define N to be the setwise stabilizer of X in G, Z to be the pointwise stabilizer, and C=N/Z. Then restriction defines a homomorphism from the algebra of G-invariant polynomial functions on V to the algebra of C-invariant functions on X. In my thesis, I extend earlier work by Douglass and Rohrle for Coxeter groups to the case where G is a complex reflection group of type G(r,p,n) in the notation of Shephard and Todd and X is in the lattice of the reflection arrangement of G. The main result characterizes when the restriction mapping is surjective in terms of the exponents of G and C and their reflection arrangements.