Molien function and calculation of invariant polynomials for space groups

  • Marko V. Jarić
  • Joseph L. Birman
Contributed Papers III. Broken Symmetry and Phase Transitions
Part of the Lecture Notes in Physics book series (LNP, volume 79)


We have developed an algorithm for the computation of the Molien function (generating for the multiplicity of the identity representation in the symmetrized nth power of representation P of group G) and used it to compute the Molien function for irreducible representations of crystal space groups. The calculation is illustrated upon some irreducible representations of the crystal space groups. Ir. particular, a case of interest is some irreducible representations of the crystal space group 0 h 3 -Pn3m. Quartic invariants are exhibited for irreducible representations *X (j) and *R (j)j= 1,2,3,4 of 0 O h 3 .


Irreducible Representation Identity Representation Finite Order Trivial Representation Symmetrize Product 
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  1. (1).
    W. Burnside, Theory of Groups of Finite Order (Dover, New York 1952) and references to Molien's papers therein.Google Scholar
  2. (2).
    M.V. Jarić and J.L. Birman, J. Math. Phys. 18, 1456, 1459, (cf. Errata) (1977).Google Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • Marko V. Jarić
    • 1
  • Joseph L. Birman
    • 1
  1. 1.Physics DepartmentCity College, C..U. N. Y.New York

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