MS Seminar (Mathematics - String Theory)

Speaker: Colin Ingalls (U New Brunswick)
Title: Noncommutative resolutions of discriminants of reflection groups
Date: Wed, Jun 29, 2016, 12:15 - 13:15
Place: Seminar Room B
Abstract: This is joint work with R. Buchweitz and E. Faber. Let $W$ be subgroup of $\rm{GL}(V)$ generated by reflections. Let $S = k[V]$ be the polynomial ring and let $z \in S$ cut out the hyperplane arrangement of mirrors in $V.$ The discriminant is the image of the hyperplane arrangement in the quotient $V/W$ which is cut out by $z^2$. Let $A$ be the skew group algebra $W \rtimes k[V]. Let e be the idempotent of kG corresponding to the trivial representation. Our main result is that
$$ End_{S^W}(S/zS) = A/AeA $$ forms a noncommutative resolution of the discriminant since it is Koszul, has global dimension $\rm{dim} V -1$.