Abstract: When we consider the linear action of a finite group on a polynomial ring, an invariant is a polynomial unchanged by the action. Noether’s Degree Bound states that in characteristic zero the maximal degree of a minimal generating invariant polynomial is bounded above by the order of the group. Derksen showed that the generators of the Hilbert ideal can be found via elimination theory from the vanishing ideal of a subspace arrangement. We show that the same approach works over the exterior algebra and prove Noether’s Degree Bound in this context. Our methods rely on a bound on the Castelnuovo-Mumford regularity of intersections of linear ideals in the exterior algebra, which we proved in previous work using tools from combinatorial representation theory.  We also show a transference of stable bounds from the symmetric algebra to the exterior algebra. A bound on invariant skew polynomials in the exterior algebra also bounds some square-free invariants in the (-1)-skew algebra and motivates future investigations in the theory of skew polarization. 

3:00pm, 511 Lake Hall,  Francesca Gandini (Kalamazoo College)