D-functions and immanants of unitary matrices and submatrices

  title={D-functions and immanants of unitary matrices and submatrices},
  author={Hubert de Guise and Dylan Spivak and Justin Kulp and Ish Dhand},
  journal={Journal of Physics A: Mathematical and Theoretical},
Motivated by recent results in multiphoton interferometry, we expand a result of Kostant on immanants of an arbitrary m × m unitary matrix T ∈ SU ( m ) ?> to the submatrices of T. Specifically, we show that immanants of principal submatrices of a unitary matrix T are a sum ∑ t D tt ( λ ) ( &OHgr; ) ?> of the diagonal D-functions of group element Ω, with t determined by the choice of submatrix, and the irrep (λ) determined by the immanant under consideration. We also provide evidence that this… 

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