In terms of just the knot polynomials, there's a simple explanation for what's going on that makes gl(1|1) $\mathfrak{gl}(1|1)$ seem totally in place:

The knot polynomial attached to the defining representation of gl(m|n) $\mathfrak{gl}(m|n)$ only depends on m-n (the dimension of that representation in the categorical sense); you just get the specialization of HOMFLY at t=qm-n. $t=q^{m-n}$.

Furthermore, nothing much interesting happens at negative values, since they're basically the same as positive ones. So, our current techniques, which work for gl(n) $\mathfrak{gl}(n)$ knot homology, can't get at dimension 0, which can be minimally described as gl(1|1). $\mathfrak{gl}(1|1)$.

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In terms of just the knot polynomials, there's a simple explanation for what's going that makes gl(1|1) seem totally in place:

The knot polynomial attached to the defining representation of gl(m|n) only depends on m-n (the dimension of that representation in the categorical sense); you just get the specialization of HOMFLY at t=qm-n.

Furthermore, nothing much interesting happens at negative values, since they're basically the same as positive ones. So, our current techniques, which work for gl(n) knot homology can't get at dimension 0, which can be minimally described as gl(1|1).