nLab immanant

Idea

This is a joint generalization of determinants and permanents.

If $A = (a_{i,j}) \in \mathcal{M}_{n,p}(R)$ where $R$ is a commutative ring and if $\lambda \vdash n$ is a partition of $n$, we define:

$$Imm_{\lambda}(A) = \underset{\sigma \in \mathfrak{S}_{n}}{\sum}\chi_{\lambda}(\sigma)a_{i,\sigma(i)}$$

where $\chi_{\lambda}$ is the character of the irreducible representation of the symmetric group $\mathfrak{S}_{n}$ associated to $\lambda$.

Related entries

• determinant
• permanent

References

• Wikipedia entry