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Ïîëíàÿ âåðñèÿ
ÆÓÐÍÀËÛ // Symmetry, Integrability and Geometry: Methods and Applications
SIGMA, 2006, òîì 2, 006, 60 ñòð. (Mi sigma34)
Orbit Functions
Anatoliy Klimyk, Jiri Patera

Ñïèñîê ëèòåðàòóðû
1. Patera J., “Orbit functions of compact semisimple Lie groups as special functions”, Proceedinds of Fifth International Conference “Symmetry in Nonlinear Mathematical Physics”, Part 3 (June 23–29, 2003, Kyiv), Proceedings of Institute of Mathematics, 50, eds. A. G. Nikitin, V. M. Boyko, R. O. Popovych and I. A. Yehorchenko, Kyiv, 2004, 1152–1160  mathscinet  zmath
2. Vilenkin N. Ja., Klimyk A. U., Representations of Lie groups and special functions, Vols. 1–3, Kluwer, Dordrecht, 1991–1993  mathscinet  zmath
3. Miller W., Lie theory and special functions, Academic Press, New York, 1968  mathscinet  zmath
4. Vilenkin N. Ja., Special functions and the theory of group representations, Amer. Math. Soc., Providence RI, 1968  mathscinet  zmath
5. Macdonald I. G., Symmetric functions and Hall polynomials, 2nd ed., Oxford Univ. Press, Oxford, 1995  mathscinet  zmath
6. Macdonald I. G., “A new class of symmetric functions”, B20a, Sémin. Lothar. Comb., 20, Publ. I.R.M.A., Strasbourg, 1988, 41 p.
7. Macdonald I. G., “Orthogonal polynomials associated with root systems”, B45a, Séminaire Lotharingien de Combinatoire, 45, Strasbourg, 2000, 40 p.  mathscinet  zmath
8. Vilenkin N. Ja., Klimyk A. U., Representations of Lie groups and special functions: recent advances, Kluwer, Dordrecht, 1995  mathscinet
9. Moody R. V., Patera J., “Computation of character decompositions of class functions on compact semisimple Lie groups”, Math. Comp., 48 (1987), 799–827  crossref  mathscinet  zmath  isi
10. Moody R. V., Patera J., “Elements of finite order in Lie groups and their applications”, XIII Int. Colloq. on Group Theoretical Methods in Physics, ed. W. Zachary, World Scientific Publishers, Singapore, 1984, 308–318  mathscinet
11. McKay W. G., Moody R. V., Patera J., “Tables of $E_8$ characters and decomposition of plethysms”, Lie Algebras and Related Topics, eds. D. J. Britten, F. W. Lemire and R. V. Moody, Amer. Math. Society, Providence R.I., 1985, 227–264  mathscinet
12. McKay W. G., Moody R. V., Patera J., “Decomposition of tensor products of $E_8$ representations”, Algebras Groups Geom., 3 (1986), 286–328  mathscinet  zmath
13. Patera J., Sharp R. T., “Branching rules for representations of simple Lie algebras through Weyl group orbit reduction”, J. Phys. A: Math. Gen., 22 (1989), 2329–2340  crossref  mathscinet  zmath  adsnasa
14. Grimm S., Patera J., “Decomposition of tensor products of the fundamental representations of $E_8$”, CRM Proc. Lecture Notes, 11 (1997), 329–355  mathscinet  zmath
15. Atoyan A., Patera J., “Properties of continuous Fourier extension of the discrete cosine transform and its multidimensional generalization”, J. Math. Phys., 45 (2004), 2468–2491  crossref  mathscinet  zmath  adsnasa  isi; arXiv:math-ph/0309039  mathscinet
16. Rao K. R., Yip P., Discrete cosine transform – algorithms, advantages, applications, Academic Press, New York, 1990  mathscinet
17. Kane R., Reflection groups and invariants, Springer, New York, 2002
18. Humphreys J. E., Reflection groups and Coxeter groups, Cambridge Univ. Press, Cambridge, 1990  mathscinet
19. Humphreys J. E., Introduction to Lie Algebras and Representation Theory, Springer, New York, 1972  mathscinet  zmath
20. Pinsky M. A., “The Eigenvalues of an Equilateral Triangle”, SIAM J. Math. Anal., 11 (1980), 819–827  crossref  mathscinet  zmath  isi
21. Patera J., Algebraic solution of the Neumann boundary problems on fundamental regions of a compact semisimple Lie group, Preprint, CRM, Montreal, 2003  zmath
22. Patera J., “Compact simple Lie groups and their $C$-, $S$-, and $E$-transforms”, SIGMA, 1 (2005), paper 025, 6 pp., ages  mathnet  mathscinet  zmath; arXiv:math-ph/0512029
23. Bremner M. R., Moody R. V., Patera J., Tables of dominant weight multiplicities for representations of simple Lie algebras, Marcel Dekker, New York, 1985  mathscinet  zmath
24. McKay W. G., Patera J., Rand D. W., Tables of representations of simple Lie algebras, CRM, Montreal, 1990  mathscinet
25. Champagne B., Kjiri M., Patera J., Sharp R. T., “Description of reflection generated polytopes using decorated Coxeter diagrams”, Can. J. Phys., 73 (1995), 566–584  adsnasa  isi
26. Moody R. V., Patera J., “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  crossref  mathscinet  zmath  adsnasa
27. McKay W. G., Patera J., Sannikoff D., “The computation of branching rules for representations of semisimple Lie algebras”, Computers in Nonassociative Rings and Algebras, eds. R. E. Beck and B. Kolman, Academic Press, New York, 1977, 235–278  mathscinet
28. Gingras F., Patera J., Sharp R. T., “Orbit-orbit branching rules between simple low-rank algebras and equal-rank subalgebras”, J. Math. Phys., 33 (1992), 1618–1626  crossref  mathscinet  zmath  adsnasa  isi
29. Patera J., Sharp R. T., “Branching rules for representations of simple Lie algebras through Weyl group orbits reduction”, J. Phys. A: Math. Gen., 22 (1989), 2329–2340  crossref  mathscinet  zmath  adsnasa
30. Patera J., Zaratsyan A., “Discrete and continuous cosine transform generalized to Lie groups $SU(2)\times SU(2)$ and $O(5)$”, J. Math. Phys., 46 (2005), 053514, 25 pp., ages  crossref  mathscinet  zmath  adsnasa  isi
31. Patera J., Zaratsyan A., “Discrete and continuous cosine transform generalized to Lie groups $SU(2)$ and $G_2$”, J. Math. Phys., 46 (2005), 113506, 17 pp., ages  crossref  mathscinet  zmath  adsnasa  isi
32. Lemire F. W., Patera J., “Congruence number, a generalisation of $SU(3)$ triality”, J. Math. Phys., 21 (1980), 2026–2027  crossref  mathscinet  zmath  adsnasa  isi
33. Zhelobenko D. P., Compact Lie groups and their representations, Nauka, Moscow, 1970  mathscinet  zmath
34. McKay W. G., Patera J., Tables of dimensions, indices and branching rules for representations of simple Lie algebras, Marcel Dekker, New York, 1981  mathscinet  zmath
35. Strang G., “The discrete cosine transform”, SIAM Review, 41 (1999), 135–147  crossref  mathscinet  zmath  isi
36. Kac V., “Automorphisms of finite order of semisimple Lie algebras”, J. Funct. Anal. Appl., 3 (1969), 252–255  crossref  mathscinet
37. Moody R. V., Patera J., “Characters of elements of finite order in simple Lie groups”, SIAM J. Algebraic Discrete Methods, 5 (1984), 359–383  crossref  mathscinet  zmath
38. McKay W. G., Moody R. V., Patera J., Pianzola A., “The 785 conjugacy classes of rational elements of finite order in $E_8$”, Contemp. Math., 110 (1990), 79–123  mathscinet  zmath
39. Heckman G. J., Opdam E. M., “Root systems and hypergeometric functions. I”, Compos. Math., 64 (1987), 329–352  mathscinet  zmath  isi
40. Heckman G. J., “Root systems and hypergeometric functions. II”, Compos. Math., 64 (1987), 353–373  mathscinet  zmath  isi
41. Gasper G., Rahman M., Basic hypergeometric functions, Cambridge Univ. Press, Cambridge, 1990  mathscinet  zmath

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