On multidimensional analogs of Euler (Tait-Bryan) angles and Grassmannians

M. V. Babich^a, L. A. Bordag^b, A. M. Khvedelidze^cde, D. M. Mladenov<sup>f

a</sup> St. Petersburg Department of V. A. Steklov Institute of Mathematics, St. Petersburg, Russia
^b Joint Insatitute for Nuclear Research, Dubna, 141980, Russia
^c A. Razmadze Mathematical Institute, Iv. Javakhishvili Tbilisi State University
^d Institute of Quantum Physics and Engineering Technologies, Georgian Technical University, Tbilisi, Georgia
^e Meshcheryakov Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna, 141980, Moscow Region, Russia
^f Sofia University “St. Kliment Ohridski”, 1164 Sofia, Bulgaria

Abstract: We present a generalization of the well known Euler angles method, or more precisely its modification the Tait-Bryan angles method, describing the rotation of an orthogonal frame in $\mathbb R^3$. The newly developed system of elementary unitary rotations allows to introduce convenient parameterization in high-dimensional complex-valued unitary spaces. As a by-product we obtain parametrization of the affine parts of Grassmannians and a parameterization of the algebraically-open subsets of conjugation classes of Hermitian matrices by elementary rotations. The parametrization of these objects has many applications especially in quantum information theory.

Key words and phrases: Lie groups, unitary group, Grassmanians.

UDC: 514.85, 514.74

Received: 19.09.2025

Language: English