Friday, March 10 2017
16:00 - 17:00

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.

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