dc.contributor.author Chillingworth, D.R.J. dc.contributor.author Lauterbach, R. dc.contributor.author Turzi, S.S. dc.date.accessioned 2016-06-13T13:33:50Z dc.date.available 2016-06-13T13:33:50Z dc.date.issued 2015-12-31 dc.identifier.issn 1751-8113 dc.identifier.uri http://hdl.handle.net/20.500.11824/247 dc.description.abstract We investigate the invariants of the 25-dimensional real representation of the group SO(3) ? Z2 given by the left and right actions of SO(3) on 5 5 matrices together with matrix transposition; the action on column vectors is the irreducible five-dimensional representation of SO(3). The 25-dimensional representation arises naturally in the study of nematic liquid crystals, where the second-rank orientational order parameters of a molecule are represented by -rfaut symmetric 3 Ã—3 traceless symmetric matrix, and where a rigid rotation in R3 induces a linear transformation of this space of matrices. The entropy contribution to a free energy density function in this context turns out to have SO(3) ? Z2 symmetry. Although it is unrealistic to expect to describe the complete algebraic structure of the ring of invariants, we are able to calculate as a rational function the Molien series that gives the number of linearly independent invariants at each homogeneous degree. The form of the function indicates a basis of 19 primary invariants and suggests there are N = 1 453 926 048 linearly independent secondary invariants; we prove that their number is an integer multiple of N 4. The algebraic structure of invariants up to degree 4 is investigated in detail. dc.format application/pdf dc.language.iso eng en_US dc.rights Reconocimiento-NoComercial-CompartirIgual 3.0 España en_US dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/es/ en_US dc.subject invariants dc.subject Molien series dc.subject order parameters dc.subject supertensors dc.subject wreath product dc.title Molien series and low-degree invariants for a natural action of $SO(3) \wr Z_2$ dc.type info:eu-repo/semantics/article en_US dc.identifier.doi 10.1088/1751-8113/48/1/015203 dc.relation.publisherversion http://iopscience.iop.org/article/10.1088/1751-8113/48/1/015203/meta dc.rights.accessRights info:eu-repo/semantics/openAccess en_US dc.type.hasVersion info:eu-repo/semantics/acceptedVersion en_US dc.journal.title Journal of Physics A: Mathematical and Theoretical en_US
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