#### Hall 123

#### Polynomial invariants of finite reflection groups

#### Mrigendra Singh Kushwaha

##### IMSc, Chennai

*If W is a finite reflection subgroup of GL(V), it acts in a natural way on the ring of polynomial functions on V, where V is real vector space of dim n. I will prove Chevalley's Theorem, which proves that sub algebra of invariant polynomials generated as an R-algebra by n homogeneous algebraically independent polynomials of positive degree (together with 1). Next i will show connection of degrees of invariant polynomials with reflection group. Lastly a theorem of Shephard and Todd, which asserts that the only for reflection groups can the ring of invariants be generated by algebraically independent polynomials.*

Done