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Bernstein-Gelfand-Gelfand meets geometric complexity theory: resolving the 2 x 2 permanents of a 2 x n matrix
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abstract
We describe the minimal free resolution of the ideal of $2 \times 2$ subpermanents of a $2 \times n$ generic matrix $M$. In contrast to the case of $2 \times 2$ determinants, the $2 \times 2$ permanents define an ideal which is neither prime nor Cohen-Macaulay. We combine work of Laubenbacher-Swanson on the Gr\"obner basis of an ideal of $2 \times 2$ permanents of a generic matrix with our previous work connecting the initial ideal of $2 \times 2$ permanents to a simplicial complex. The main technical tool is a spectral sequence arising from the Bernstein-Gelfand-Gelfand correspondence.
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Cited by 1 Pith paper
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Equivariant Syzygies of the Ideal of 2 x 2 Permanents of a 2 x n Matrix
The syzygies of the ideal of 2x2 permanents of a 2xn matrix are described as explicit representations of the symmetric group and torus actions.
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