For positive integers , we compute the -equivariant description of the local cohomology modules of the polynomial ring with support in the ideal of minors of the generic matrix. Our techniques allow us to explicitly compute all the modules , for a partition and the ideal generated by the irreducible subrepresentation of indexed by . In particular we determine the regularity of the ideals , and we deduce that the only ones admitting a linear free resolution are the powers of the ideal of maximal minors of the generic matrix, as well as the products between such powers and the maximal ideal of .
"Local cohomology with support in generic determinantal ideals." Algebra Number Theory 8 (5) 1231 - 1257, 2014. https://doi.org/10.2140/ant.2014.8.1231