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dc.contributor.authorChillingworth, D.R.J.
dc.contributor.authorLauterbach, R.
dc.contributor.authorTurzi, S.S.
dc.date.accessioned2016-06-13T13:33:50Z
dc.date.available2016-06-13T13:33:50Z
dc.date.issued2015-12-31
dc.identifier.issn1751-8113
dc.identifier.urihttp://hdl.handle.net/20.500.11824/247
dc.description.abstractWe 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 ×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.
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dc.language.isoengen_US
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.subjectinvariants
dc.subjectMolien series
dc.subjectorder parameters
dc.subjectsupertensors
dc.subjectwreath product
dc.titleMolien series and low-degree invariants for a natural action of $SO(3) \wr Z_2$
dc.typeinfo:eu-repo/semantics/articleen_US
dc.identifier.doi10.1088/1751-8113/48/1/015203
dc.relation.publisherversionhttp://iopscience.iop.org/article/10.1088/1751-8113/48/1/015203/meta
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessen_US
dc.type.hasVersioninfo:eu-repo/semantics/acceptedVersionen_US
dc.journal.titleJournal of Physics A: Mathematical and Theoreticalen_US


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