Robert Vaughan MOODY



  1. (with Xinghua Deng):
    Dworkin's argument revisited: Point Processes, Dynamics, Diffraction, and Correlations.
    Preprint, March 2007 .

  2. (with Jeong-Yup Lee):
    Deforming model sets.
    Preprint, March 2007.

  3. (with Michael Baake and Manuela Huer):
    Similar sublattices of the root lattice A4.
    Preprint, February 2007 .

  4. (with Jiri Patera):
    Orthogonality with families of C-, S-, E-functions of any compact semisimple Lie group.
    Symmetry, Integrability and Geom.: Methods and Applications , Vol. 2 (2006), Paper 076.

  5. (with Michael Baake and Daniel Lenz):
    Characterization of model sets by dynamical systems.
    Ergod. Th. Dynam. Sys., 26 (2006) to appear.

  6. : Long-range order and diffraction.
    Proceedings of a Conference on Groups and Lie Algebras, Ed. Ken-Ichi Shinoda,
    Sophia Kokyuroku in Mathematics, 46, 2006  .

  7. (with Jeong-Yup Lee):
    A Chararacterization of Model Multi-colour Sets.
    Annales Inst. Hénri Poincaré 7 (2006), 125-143.

  8. Alice Boner and the Geometry of Temple Cave Art in India.
    Proceedings of the 2005 Bridges Conference (Renaissance Banff),
    Ed. Reza Sarhangi and Robert V. Moody, 2005
    Bridges: Mathematical Connections in Art, Music, and Science.

  9. Mathematical Quasicrystals: A Tale of Two Topologies.
    Preprint, to appear in the
    Proceedings of the International Congress of Mathematical Physics, Lisbon, 2003.

  10. (with M. Baake):
    Pure Point Diffraction,
    J. of Non-crystaline Solids, 334&335 (2004) 77-82.

  11. (with N. Strungaru):
    Point Sets and Dynamical Systems in the Autocorrelation Topology,
    Can. Math. Bull. 47(2004), 82-99.

  12. (with M. Baake, C. Richard and B. Sing):
    Which distributions of matter diffract? – Some answers.
    In: Quasicrystals , Ed. H.-R. Trebin, Wiley-VCH, Weinheim, 2003, 188-207.

  13. (with Jeong-Yup Lee and B. Solomyak):
    Consequences of Pure Point Diffraction Spectra for Multiset Substitution Systems,
    Discrete and Computational Geometry, 29 (2003) 525-560.

  14. (with Jeong-Yup Lee and B. Solomyak):
    Pure Point Dynamical and Diffraction Spectra,   Annales Inst. Hénri Poincaré, 3 (2002) 1003-1018.

  15. (with M. Baake and U. Grimm):
    Die verborgene Ordnung der Quasikristalle.
    Spektrum der Wissenschaften, Feb. 2002, 64-74.
    English translation: What is aperiodic order? arXiv:math.HO/0203252

  16. (with M. Baake):
    Weighted Dirac combs with pure point diffraction,   Journal für die reine und angewandte Mathematik (Crelle's Journal),
    573 (2004), 61-94.

  17. Uniform Distribution in Model Sets, Can. Math. Bull.,   45 (1) (2002), 123-130.

  18. (with Jeong-Yup Lee):
    Lattice Substitution Systems in Model Sets, Discrete and Computational Geometry, 25 (2001), 173-201.

  19. (with M. Baake):
    Self-similar Measures for Quasicrystals. In Directions in Mathematical Quasicrystals, ed. M. Baake and R.V. Moody, CRM Monograph Series, AMS, Providence, RI, 2000, pp. 1-42.

  20. (with J. Morita):
    Positivity for K1 and K2. J. Algebra, 229 (2000) 1-24.

  21. (with M. Baake and P. Pleasants):
    Diffraction from the visible lattice points and the kth power-free integers. J. Discrete and Computational Mathematics, 221 (2000) 3-42.

  22. (with M. Baake):
    Similarity Submodules and Root Systems in Four Dimesions. Can. J. Math., 51 (1999) 1258-1276.

  23. Model sets: A Survey. In: From Quasicrystals to More Complex Systems, eds. F. Axel, F. Dénoyer, J.P. Gazeau, Centre de physique Les Houches, Springer Verlag, 2000, pp.

  24. (with M. Baake):
    Diffractive point sets with entropy. J. Phys. A: Math. Gen., 31 (1999) 1258-1276.

  25. (with M. Baake and M. Schlottmann):
    Limit-(quasi)periodic point sets as quasicrystals with p-adic internal spaces. J. Phys. A: Math. Gen., 31 (1998) 5755-5765.

  26. (with M. Baake):
    Multi-component model sets and invariant densities. In Aperiodic '97, eds. M. de Boissieu, J.-L. Verger-Gaugry, and R. Currat, World Scientific, Singapore, 1998, pp. 9-20.

  27. (with M. Baake):
    Invariant submodules and semigroups of self-similarities for Fibonacci modules. In: Aperiodic '97, eds. M. de Boissieu, J.-L. Verger-Gaugry, and R. Currat, World Scientific, Sigapore, 1998, pp. 21-27.

  28. (with C. Hohnecker, P. Kramer and Z. Papadopolis):
    Canonical icosahedral quasicrystals for the F-phase generated by coherent phases in physical space. J. Phys. A: Math. Gen., 30 (1997) 6493-6507.

  29. (with M. Baake):
    Similarity submodules and semigroups. In: Quasicrystals and Discrete Geometry, ed. J. Patera, Comm. Fields Institute, AMS, Providence, RI, 1998, pp. 1-13.

  30. (with M. Baake):
    Self-similarities and invariant densities for model sets. In Algebraic methods and theoretical physics, ed. Y. Saint-Aubin, Springer, New York, 2000. pp.

  31. (with J. Patera):
    Minimal distances, densities, and coverings of quasicrytals. Comm. Math. Phys., 195 (1998) 613-626.

  32. (with L. Chen and J. Patera):
    Non-crystallographic root systems. In: Quasicrystals and Discrete Geometry, ed. J. Patera, Comm. Fields Institute, 10, AMS, Providence, RI, 1998.

  33. (with A. Pianzola):
    Kac-Moody Lie algebras: a survey of their algebraic development over the first 30 years. In: Canadian Mathematical Society 1945-1995, eds. J.B. Carrell and R. Murty, CMS, Ottawa, ON, 1996, pp. 211-245.

  34. Meyer Sets and Their Duals. In The Mathematics of Aperiodic Order, Proceedings of the NATO-Advanced Study Institute on Long-range Aperiodic Order, ed. R.V. Moody, NATO ASI Series C489, Kluwer Acad. Press, 1997. pp. 403-441.

  35. (with Hohnecker, P. Kramer, Z. Papadopolis):
    Generation of 3D icosahedral quasicrystals by matching phases in physical space. Proc. 5th Int. Conf. on Quasicrystals, eds. C. Janot and R. Mosseri, World Scientific, Singapore 1995, pp. 112-115.

  36. (with J. Patera):
    Dynamical generation of quasicrystals. Letters in Mathematical Physics, 36 (1996) 291-300.

  37. Meyer sets and the finite generation of quasicrystals. Symmetries in Science VIII, ed. B. Gruber, Plenum Press, New York, 1995.

  38. (with A. Weiss):
    On shelling E8 quasicrystals. J. Number Theory. 47 (1994) 405-412.

  39. (with J. Patera):
    Voronoi domains and dual cells in the generalized kaleidoscope with applications to root and weight lattices. Can. J. Math., 47 (1995) 573-605.

  40. (with J. Patera):
    Colourings of quasicrystals. Can. J. Phys., 72 (1994) 442-452.

  41. (with S. Berman):
    The algebraic theory of quasicrystals with 5-fold symmetries. J. Phys. A: Math. Gen., 27 (1994) 115-129.

  42. (with M. Fabbri):
    Irreducible representations of Virasoro-toroidal Lie algebras. Comm. in Math. Phys., 159 (1994) 1-13.

  43. (with S. Eswara Rao):
    Vertex representations for n-toroidal Lie algebras and a generalization of the Virasoro algebras. Comm. in Math. Phys., 159 (1994) 239-264.

  44. (with J. Patera): Quasicrystals and icosians. J. Phys. A: Math. Gen., 26 (1993) 2829-2853.

  45. (with J. Patera):
    A Coxeter diagram description of faces of Voronoi cells and their duals. Proc. XIX International Symposium on Group Theoretical Methods in Physics, 1992.

  46. (with J. Patera):
    Voronoi and Delaunay cells of root lattices: classification of their faces and facets by Coxeter-Dynkin diagrams. J. Phys. A: Math. Gen., 25 (1992) 5089-5134.

  47. (with S. Eswara Rao and T. Yokonuma):
    Lie algeras and Weyl groups arising from vertex operator representations. Nova J. of Algebras and Geometries, 1 (1992) 15-57.

  48. (with Z. Shi):
    Toroidal Weyl groups. Nova J. of Algebra and Geometries, 1 (1992) 317-337.

  49. (with S. Berman):
    Lie algebras graded by finite root systems and the intersection matrix algebras of Slodowy. Inventiones Mathematicae, 108 (1992) 323-347.

  50. (with J. Patera):
    Discrete and continuous graded contractions of representations of Lie algebras. J. Phys. A: Math. Gen., 24 (1991) 2227-2257.

  51. (with W. McKay, J. Patera and A. Pianzola):
    The 785 conjugacy classes of rational elements of finite order in E8. Contemporary Mathematics, 110 (1990) 79-123.

  52. (with S. Rao and T. Yokonuma):
    Toroidal Lie algebras and vertex representations. Geometriae Dedicata, 35 (1990) 283-307.

  53. (with J. Bliss and A. Pianzola):
    Appendix to elliptic genera, involutions and homogeneous spin manifolds by Friedrich Hirzebruch and Peter Slodowy. Geometriae Dedicata, 35 (1990) 345-351.

  54. (with A. Pianzola):
    On infinite root systems. Trans. Amer. Math. Soc., 315 (1989) 661-696.

  55. (with S. Berman and Y.S. Lee):
    The spectrum of a Coxeter transformation, affine Coxeter transformations and the defect map. J. Algebra, 121 (1989) 339-357.

  56. (with V. Kac and M. Wakimoto):
    On E10, Differential Geometrical Methods in Theoretical Physics. Kluwer Acad. Pub., 1988.

  57. (with W.G. McKay, J. Patera and A. Pianzola):
    The 785 conjugacy classes of rational elements of finite order in E8. Proc. Conf. on Lie Algebras and Related Topics, Madison, WI, 1988.

  58. (with A. Pianzola):
    Infinite dimensional Lie algebras: an overview. Algebras, Groups and Geometries, 4 (1987) 165-213.

  59. (with J. Patera):
    Computation of character decompositions of class functions on compact semi-simple Lie groups. Mathematics of Computation, 48 (1987) 799-827.

  60. (with W.G. McKay and J. Patera):
    Decomposition of tensor products of E8 representations. Algebras, Groups and Geometries, 3 (1986) 286-328.

  61. (with G. Benkart):
    Derivations, central extensions and affine Lie algebras. Algebras, Groups and Geometries, 3 (1986) 456-492.

  62. (with J. Patera and W.G. McKay):
    Table of E8 characters and decompositions of plethysms, Lie algebras and related topics. CMS Conference Proceedings, 5 (1986).

  63. (with M. Nicolescu, J. Patera and Sai Pin):
    Verma bases for modules of classical simple Lie algebras. J. Math. Phys., 27 (1986) 668-677.

  64. Generalized root systems and characters. Contemporary Mathematics, 45 (1985) 245-269.

  65. (with J. Patera):
    Elements of finite order in simple Lie groups and their applications. Proc. Conf. on Group Theoretical Methods in Physics (1984).

  66. (with J. Patera):
    Characters of elements of finite order in Lie groups. SIAM Journal for Algebraic and Discrete Methods, 5 (1984) 359-383.

  67. (with J. Patera):
    General charge conjugation operators in simple Lie groups. J. Math. Phys., 25 (1984) 2838-2847.

  68. (with J. Patera and R. Sharp):
    Character generators for elements of inite order in simple Lie groups A1, A2, A3, B2 and G2. J. Math. Phys., 24 (1983) 2387-2396.

  69. (with A. Pianzola):
    Lamda-mappings between representation rings of Lie algebras. Can. J. Math. 23 (1983) 898-960.

  70. (with J. Patera):
    Fast recursion formula for weight multiplicities. Bull. Amer. Math. Soc., 7 (1982) 237-242.

  71. (with T. Yokonuma):
    Root systems and cartan matrices. Can. J. Math., 34 (1982), 63-79.

  72. Lie algebra subjoining mathematical reports. Academy of Science Canada, 2 (1980), 259-264.

  73. Isomorphisms of upper cartan-matrix Lie algebras. Proc. of the London Mathematical Society, XL (1980) 430-442.

  74. (with J. Lepowsky):
    Hyperbolic Lie algebras and quasi-regular cusps on Hilbert modular surfaces. Mathematische Annalen, 245 (1979) 63-88.

  75. (with S. Berman):
    Lie algebra multiplicities. Proc. Amer. Math. Soc., 76 (1979) 223-228.

  76. Root systems of hyperbolic type. Advances in Mathematics, 33 (1979) 144-160.

  77. Polynomial invariants of isometry groups of indefinite quadratic lattices. Tohoku J. of Mathematics, 30 (1978) 525-535.

  78. Macdonald identities and Euclidean Lie algebras. Proc. Amer. Math. Soc., 48 (1975) 43-52.

  79. (with S. Berman):
    Extensions of Chevalley groups. Israel J. Math., 22 (1975) 42-51.

  80. (with K.L. Teo):
    Tits' systems with crystallographic Weyl groups. J. Algebra, 21 (1972) 178-190.

  81. (with S. Berman and M. Wonenburger):
    Cartan matrices with null roots and finite cartan matrices. Indiana Mathematics Journal, 21 (1972) 1091-1099.

  82. Simple quotients of Euclidean Lie algebras. Can. J. Math., 22 (1970) 839-846.

  83. Euclidean Lie algebras. Can. J. Math., 21 (1969) 1432-1454.

  84. A new class of Lie algebras. J. Algebra, 10 (1968) 211-230

  85. Lie algebras associated with generalized cartan matrices. Bull. Amer. Math. Soc., 73 (1967) 217-221.


  1. Euclidean Lie algebras. Can. J. Math., 21 (1969) 1432-1454. (Re-publication of this paper in Selected Papers from the Canadian Journal of Mathematics.) 1996.

  2. Hausdorff-Banach-Tarski paradox. La Gazette des Sciences Mathematiques du Québec, XIV (1991) 13-29.


  1. co-editor (with M. Baake):
    Directions in Mathematical Quasicrystals, CRM Monograph Series, AMS, Providence, RI, 2000.

  2. editor:
    The Mathematics of Aperiodic Order, Proceedings of the NATO Advanced Study Institute on long-range aperiodic order. Kluwer Acad. Publ., 1997.

  3. (with A. Pianzola):
    Lie algebras with triangular decompositions. Canadian Mathematical Society Series, John Wiley Publishers, 1995.

  4. (with J. Patera, R. Slansky and S. Kass):
    Affine Lie algebras, weight multiplicities and branching rules. University of California Press, 1991, 2 volumes, 897 pp.

  5. (edited with D.J. Britten and F.W. Lemire):
    Lie algebras and related topics. CMS Conference Proceedings, Vol. 5, AMS, 1986.

  6. (with M. Bremner and J. Patera): Tables of weight space multiplicities. Marcel Dekker, 1983, 340 pp.