Syzygies of determinantal thickenings and representations of the general linear Lie superalgebra
Abstract
We let S denote the ring of polynomial functions on the space of m x n matrices, and consider the action of the group GL = GL_m x GL_n via row and column operations on the matrix entries. For a GLinvariant ideal I in S we show that the linear strands of its minimal free resolution translate via the BGG correspondence to modules over the general linear Lie superalgebra gl(mn). When I is the ideal generated by the GLorbit of a highest weight vector, we give a conjectural description of the classes of these gl(mn)modules in the Grothendieck group, and prove that our prediction is correct for the first strand of the minimal free resolution.
 Publication:

arXiv eprints
 Pub Date:
 August 2018
 arXiv:
 arXiv:1808.05649
 Bibcode:
 2018arXiv180805649R
 Keywords:

 Mathematics  Commutative Algebra;
 Mathematics  Representation Theory;
 13D02;
 14M12;
 17B10
 EPrint:
 To appear in Acta Mathematica Vietnamica, special issue: The Prospects for Commutative Algebra