# Brandeis University Everyperson Seminar

## Monday December 13, 2004, 4 PM, Goldsmith 317

### tea at
3:30 PM at the Math Department lounge (Goldsmith 300)

**Speaker**: Sasha Golubeva (Hebrew University)

**Title**: Linear groups-subgroups pairs with the same
invariants

**Abstract**:
We consider the problem of finding all complex linear algebraic
group-subgroup pairs such that the rational invariants of the group and
the subgroup coincide. We call them exceptional pairs.

As follows from the main theorem of Galois theory, a finite group is
uniquely determined by its invariants. In other words, if *G* is finite
and *H* is proper subgroup, then the pair *(H,G)* is not exceptional. A
classification of exceptional pairs for a certain type of groups shows to
what extent a group of this type is determined by its invariants.