Background: Symmetries are a powerful way to characterize nuclear wave functions. A true dynamical symmetry, where the Hamiltonian is block-diagonal in subspaces defined by the group, is rare. More likely is a quasidynamical symmetry: states with different quantum numbers (i.e. angular momentum) nonetheless sharing similar group-theoretical decompositions. Purpose: We use group-theoretical decomposition to investigate backbending, an abrupt change in the moment of inertia along the yrast line, in $^{48,49,50}$Cr: prior mean-field calculations of these nuclides suggest a change from strongly prolate to more spherical configurations as one crosses the backbending and increases in angular momentum. Methods: We decompose configuration-interaction shell-model wavefunctions using the SU(2) groups $L$ (total orbital angular momentum) and $S$ (total spin), and the groups SU(3) and SU(4). We do not need a special basis but only matrix elements of Casimir operators, applied with a modified Lanczos algorithm. Results: We find quasidynamical symmetries, albeit often of a different character above and below the backbending, for each group. While the strongest evolution was in SU(3), the decompositions did not suggest a decrease in deformation. We point out with a simple example that mean-field and SU(3) configurations may give very different pictures of deformation. Conclusions: Persistent quasidynamical symmetries for several groups allow us to identify the members of a band and to characterize how they evolve with increasing angular momentum, especially before and after backbending.

23 pages, 16 figures; modified after referee and editorial comments