D-functions and immanants of unitary matrices and submatrices. (21st January 2016)

• Record Type: Journal Article
• Authors: Guise, Hubert de; Spivak, Dylan; Kulp, Justin; Dhand, Ish
• Is Part Of: Journal of physics. Volume 49:Number 9(2016)
• Publication Date: 2016-01-21
• Subjects: immanants -- unitary matrices -- Wigner D-functions; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8113/49/9/09LT01
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: Motivated by recent results in multiphoton interferometry, we expand a result of Kostant on immanants of an arbitrary m × m unitary matrix to the submatrices of T . Specifically, we show that immanants of principal submatrices of a unitary matrix T are a sum 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 result extends to some submatrices that are not principal diagonal, and we discuss how this result can be extended to cases where T carries an SU( m ) representation that is different from the defining representation.