RESEARCH METHODOLOGY SEMINAR
11:45 am - 12:45 pm, Lecture Hall 1
On the Ring of Invariants of Finite Groups generated by pseudo-reflections
Shubham Ovhal
Chennai Mathematical Institute.
11-04-19

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Abstract

Invariant Theory of Linear Algbraic Groups is a classical subject that studies polynomial functions which are invariant under various Group Actions. Finite generation of these Rings is a central problem which was resolved in several cases by David Hilbert, Emmy Noether, etc. among others. Chevalley–Shephard–Todd theorem is one such result which asserts a particularly well-behaved structure for such rings, that they are Polynomial rings. We will discuss this result and look at some techniques used in the proof and roughly in the subject, e.g. uses of Hilbert-Poincaré Series, Reynolds operator, Noether's theorem on invariants, Galois Groups, etc. Time permits we will demonstrate the theorem through examples.