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- W3047372100 abstract "Let $S = mathbb{C}[x_{i,j}]$ be the ring of polynomial functions on the space of $m times n$ matrices, and consider the action of the group $mathbf{GL} = mathbf{GL}_m times mathbf{GL}_n$ via row and column operations on the matrix entries. It is proven by Raicu and Weyman that for a $mathbf{GL}$-invariant ideal $I subseteq S$, the linear strands of its minimal free resolution translates via the BGG correspondence to modules over the general linear Lie superalgebra $mathfrak{gl}(m|n)$. When $I=I_{lambda}$ is the ideal generated by the $mathbf{GL}$-orbit of a highest weight vector of weight $lambda$, they gave a conjectural description of the classes of these $mathfrak{gl}(m|n)$-modules in the Grothendieck group. We prove their conjecture here. We also give a algorithmic description of how to get the classes of these $mathfrak{gl}(m|n)$-modules for any $mathbf{GL}$-invariant ideal $I subseteq S$." @default.
- W3047372100 created "2020-08-10" @default.
- W3047372100 creator A5049216080 @default.
- W3047372100 date "2020-08-06" @default.
- W3047372100 modified "2023-09-27" @default.
- W3047372100 title "Syzygies of Determinantal Thickenings" @default.
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