University of Cambridge > Talks.cam > Kuwait Foundation Lectures > Hilbert's 14th problem and Verlinde type formulas for rings of invariant polynomials

Hilbert's 14th problem and Verlinde type formulas for rings of invariant polynomials

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I discuss the ring R of polynomials which are invariant by a mutually commutative set of n matrices. The ring of semi-invariants of binary forms is an example of the case n=1. For example it is generated by the first coefficient and the discriminant $b^2 – 4 ac$ in the quadratic case. By Gordan and Weitzenboeck the ring R is finitely generated when n=1. Despite Hilbert’s optimism, R is still no more finitely generated when n> 2. The finite generation problem is still open in the boundary case n=2. I present two non-trivial examples for which the answers are affirmative. Remarkably, these examples have Verlinde type formulas, which should be affine Lie algebra analogues of the classical Cayley-Sylvester formula.

This talk is part of the Kuwait Foundation Lectures series.

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