K V Subrahmanyam: Invariants of several matrices under SL(n) x SL(n) action
Given m, n x n matrices (X1,X2,....,Xm) with entries in a field F, the group SL(n,F) x SL(n,F) acts on this m-tuple with (A,B) sending the m tuple to (A X1 Bt, AX2Bt,... ,AXmBt). A description of the polynomial functions which are invariant under this action is well known (over infinite fields). This ring of invariant functions is known to be finitely generated. However degree bounds are poor.
Recently, based on our result on the rank of matrix families under blow-ups, Derksen and Vishwambara showed that the invariant ring is generated in degree n6 (over infinite fields).
I will describe our result, regularity under blow-ups, and the Derksen and Vishwambara result. I will also indicate how a simple calculation starting with our result yields (almost) the same bounds, without using the De...
published: 16 Mar 2016