The rings of n-dimensional polytopes

Journal of Physics A: Mathematical and Theoretical

Volumn 41, Issue 49, 2008, Pages

  Hkova L ^a   Larouche, M ^a   Patera, J ^a  

^a UNIVERSITÉ DE MONTRÉAL   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 64549147016     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/41/49/495202     Document Type: Article

References (42)

1. Humphreys J E 1990 Reflection Groups and Coxeter Groups (Cambridge: Cambridge University Press)
2. Kane R 2002 Reflection Groups and Invariants (New York: Springer)
3. Bourbaki N 1968 Groupes et algèbres de Lie (Paris: Hermann) chapters IV-VI
4. Vinberg E B and Onishchik A L 1994 Lie Groups and Lie Algebras (New York: Springer)
5. Humphreys J E 1972 Introduction to Lie Algebras and Representation Theory (New York: Springer)
6. 8 Advances in Mathematical Sciences-CRM's 25 Years (CRM Proc. Lecture Notes vol 11) ed L Vinet (Providence, RI: American Mathematical Society) pp 329-55
7. Moody R V and Patera J 1984 Characters of elements of finite order in simple Lie groups SIAM J. Algebr. Discrete Methods 5 359-83
8. Moody R V and Patera J 1987 Computation of character decompositions of class functions on compact semisimple Lie groups Math. Comput. 48 799-827
9. Moody R V and Patera J 1993 Quasicrystals and icosians J. Phys. A: Math. Gen. 26 2829-53
10. Moody R V 1997 Model sets and their duals The Mathematics of Long-Range Order (NATO ASI, Series vol C489) ed R V Moody (Dordrecht: Kluwer) pp 239-68
11. Chen L, Moody R V and Patera J 1998 Non-crystallographic root systems Quasicrystals and Discrete Geometry (Fields Institute Monograph Series vol 10) ed J Patera (Providence, RI: American Mathematical Society) pp 135-78
12. Twarock R 2002 New group structure for carbon onions and nanotubes via affine extension of non-crystallographic Coxeter groups Phys. Lett. A 300 437-44
13. Keef T and Twarock R 2008 Affine extensions of the icosahedral group with applications to the three-dimensional organization of simple viruses J. Math. Biol. (at press)
14. Gingras F, Patera J and Sharp R T 1992 Orbit-orbit branching rules between simple low-rank algebras and equal-rank subalgebras J. Math. Phys. 33 1618
15. Thoma M and Sharp R T 1996 Orbit-orbit branching rules between classical simple Lie algebras and maximal reductive subalgebras J. Math. Phys. 37 6570
16. Thoma M and Sharp R T 1996 Orbit-orbit branching rules for families of classical Lie algebra-subalgebra pairs J. Math. Phys. 37 4750
17. Bégin F and Sharp R T 1992 Weyl orbits and their expansions in irreducible representations for affine Kac-Moody algebras J. Math. Phys. 33 2343
18. Atoyan A, Patera J, Sahakian V and Akhperjanian A 2005 Fourier transform method for imaging atmospheric Cherenkov telescopes Astropart. Phys. 23 79-95
19. Dunkl C F and Y Xu 2001 Orthogonal Poynomials of Several Variables (Cambridge: Cambridge University Press)
20. Patera J 2005 Compact simple Lie groups and theirs C-, S-, and E-transforms SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) 1 025 (6 pp) (arXiv:math-ph/0512029)
21. Moody R V and Patera J 2006 Orthogonality within the families of C-, S-, and E-functions of any compact semisimple Lie group SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) 2 076 (14 pp) (arXiv:math-ph/0611020)
22. Klimyk A and Patera J 2006 Orbit functions SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) 2 006 (60 pp) (arXiv:math-ph/0601037)
23. Klimyk A and Patera J 2007 Antisymmetric orbit functions SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) 3 023 (83 pp) (arXiv:math-ph/0702040v1)
24. Klimyk A and Vilenkin N 1991 Representations of Lie Groups and Special Functions vols 1-3 (Dordrecht: Kluwer)
25. Moody R V, Nesterenko M and Patera J 2008 Computing with almost periodic functions Acta Crystallogr. A 64 654-69
26. Bremner M R, Moody R V and Patera J 1985 Tables of Dominant Weight Multiplicities for Representations of Simple Lie Algebras (New York: Marcel Dekker)
27. McKay W G and Patera J 1981 Tables of Dimensions, Indices, and Branching Rules for Representations of Simple Lie Algebras (New York: Marcel Dekker)
28. Slansky R 1981 Group theory for unified model building Phys. Rep. 79 1-128
29. Hkov L, Larouche M and Patera J Branching rules for n-dimensional Coxeter polytopes (in preparation)
30. Moody R V and Patera J 1992 Voronoi and Delaunay cells of root lattices: classification of their faces and facets by Coxeter-Dynkin diagrams J. Phys. A: Math. Gen. 25 5089-134
31. Champagne B, Kjiri M, Patera J and Sharp R T 1995 Description of reflection generated polytopes using decorated Coxeter diagrams Can. J. Phys. 73 566-84
32. Moody R V and Patera J 1995 Voronoi domains and dual cells in the generalized kaleidoscope with applications to root and weight lattices (dedicated to H S M Coxeter) Can. J. Math. 47 573-605
33. Moody R V and Patera J 1993 A description of faces of Voronoi cells and their duals Proc. 19th Int. Coll. Group Theor. Meth. in Phys. (Salamanca, 1992) vol 1 ed M del Olmo, M Santander and J Guilarte pp 438-43 (Anales de Física)
34. Lemire F W and Patera J 1980 Congruence number, a generalization of SU(3) triality J. Math. Phys. 21 2026-27
35. Patera J, Sharp R T and Winternitz P 1976 Higher indices of group representations J. Math. Phys. 17 1972-79
36. Patera J, Sharp R T and Winternitz P 1977 Higher indices of group representations J. Math. Phys. 18 1519 (erratum)
37. Gross D J and Jackiw R 1972 Effect of anomalies on quasi-renormalizable theories Phys. Rev. D 6 477-93
38. Okubo S 1977 Gauge groups without triangular anomaly Phys. Rev. D 16 3528-34
39. Sharp R T and Patera J 1981 On the triangle anomaly number of SU(n) representations J. Math. Phys. 22 2352-56
40. Borel A and Siebental J de 1949 Les sous-groupes fermés de rang maximum de groupes de Lie clos Comment Math. Helv. 23 200-21
41. Moody R V and Patera J 1984 General charge conjugation operators in simple Lie groups J. Math. Phys. 25 2838-47
42. Macdonald I G 1995 Symmetric functions and Hall polynomials 2nd edn (Oxford: Oxford University Press)