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ÆÓÐÍÀËÛ // Symmetry, Integrability and Geometry: Methods and Applications
SIGMA, 2007, òîì 3, 023, 83 ñòð. (Mi sigma149)
Antisymmetric Orbit Functions
Anatoliy Klimyk, Jiri Patera

Ñïèñîê ëèòåðàòóðû
1. Klimyk A. U., Patera J., “Orbit functions”, SIGMA, 2 (2006), 006, 60 pp., ages  mathnet  mathscinet  zmath; math-ph/0601037
2. Patera J., “Orbit functions of compact semisimple Lie groups as special functions”, Proceedings of Fifth International Conference “Symmetry in Nonlinear Mathematical Physics” (June 23–29, 2003, Kyiv), Proceedings of Institute of Mathematics, Kyiv, 50, no. 3, eds. A. G. Nikitin, V. M. Boyko, R. O. Popovych and I. A. Yehorchenko, 2004, 1152–1160  mathscinet  zmath
3. Macdonald I. G., Symmetric functions and Hall polynomials, 2nd ed., Oxford University Press, Oxford, 1995  mathscinet  zmath
4. Macdonald I. G., “A new class of symmetric functions”, Séminaire Lotharingien, 20, I.R.M.A., Strasbourg, 1988, 131–171, 372/S-20
5. Macdonald I. G., “Orthogonal polynomials associated with root systems”, Séminaire Lotharingien de Combinatoire, 45, Stracbourg, 2000, Art. B45a  mathscinet
6. Vilenkin N. Ja., Klimyk A. U., Representations of Lie groups and special functions: recent advances, Kluwer, Dordrecht, 1995  mathscinet
7. Moody R. V., Patera J., “Elements of finite order in Lie groups and their applications”, Proceedings of XIII Int. Colloq. on Group Theoretical Methods in Physics, ed. W. Zachary, World Scientific Publishers, Singapore, 1984, 308–318  mathscinet
8. 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 RI, 1985, 227–264  mathscinet
9. 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
10. 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
11. Grimm S., Patera J., “Decomposition of tensor products of the fundamental representations of $E_8$”, Advances in Mathematical Sciences – CRM's 25 Years, CRM Proc. Lecture Notes, 11, ed. L. Vinet, Amer. Math. Soc., Providence, RI, 1997, 329–355  mathscinet  zmath
12. Rao K. R., Yip P., Disrete cosine transform – algorithms, advantages, applications, Academic Press, New York, 1990  mathscinet
13. 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; math-ph/0309039  mathscinet
14. 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, 17 pp., ages  crossref  mathscinet  zmath  adsnasa  isi
15. Patera J., Zaratsyan A., “Discrete and continuous cosine transform generalized to Lie groups $SU(2)$ and $G_2$”, J. Math. Phys., 46 (2005), 113506, 25 pp., ages  crossref  mathscinet  zmath  adsnasa  isi
16. Atoyan A., Patera J., “Continuous extension of the discrete cosine transform, and its applications to data processing”, Group Theory and Numerical Analysis, CRM Proc. Lecture Notes, 39, Amer. Math. Soc., Providence, RI, 2005, 1–15  mathscinet  zmath
17. Atoyan A., Patera J., Sahakian V., Akhperjanian A., “Fourier transform method for imaging atmospheric Cherenkov telescopes”, Astroparticle Phys., 23 (2005), 79–95  crossref  adsnasa  isi; astro-ph/0409388
18. Patera J., Zaratsyan A., Zhu H.-M., “New class of interpolation methods based on discretized Lie group transform”, SPIE Electronic Imaging, 2006, 6064A-06, S1
19. Germain M., Patera J., Zaratsyan A., “Multiresolution analysis of digital images using the continuous extension of discrete group transform”, SPIE Electronic Imaging, 2006, 6065A-03, S2  adsnasa
20. Germain M., Patera J., Allard Y., “Cosine transform generalized to Lie groups $SU(2)\times SU(2)$, $O(5)$, and $SU(2)\times SU(2)\times SU(2)$: application to digital image processing”, Proc. SPIE, 6065 (2006), 387–395  adsnasa
21. 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
22. Patera J., Zaratsyan A., “Discrete and continuous sine transforms generalized to compact semisimple Lie groups of rank two”, J. Math. Phys., 47 (2006), 043512, 22 pp., ages  crossref  mathscinet  zmath  adsnasa  isi
23. Kashuba I., Patera J., Discrete and continuous exponential transforms of simple Lie groups of rank two, math-ph/0702016
24. Kane R., Reflection groups and invariants, Springer, New York, 2002
25. Humphreys J. E., Reflection groups and Coxeter groups, Cambridge University Press, Cambridge, 1990  mathscinet
26. Humphreys J. E., Introduction to Lie algebras and representation theory, Springer, New York, 1972  mathscinet  zmath
27. 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
28. Kac V., Infinite dimensional Lie algebras, Birkhäuser, Basel, 1982  mathscinet
29. Patera J., “Compact simple Lie groups and their $C$-, $S$-, and $E$-transforms”, SIGMA, 1 (2005), 025, 6 pp., ages  mathnet  mathscinet  zmath; math-ph/0512029
30. Weyl H., The classical groups, Princeton University Press, 1939  mathscinet
31. Moody R. V., Patera J., “Orthogonality within the families of $C$-, $S$-, and $E$-functions of any compact semisimple Lie group”, SIGMA, 2 (2006), 076, 14 pp., ages  mathnet  mathscinet  zmath; math-ph/0611020
32. 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
33. Zhelobenko D. P., Compact Lie groups and their representations, Nauka, Moscow, 1970  mathscinet  zmath
34. Strang G., “The discrete cosine transform”, SIAM Rev., 41 (1999), 135–147  crossref  mathscinet  zmath  isi
35. Martuchi S. A., “Symmetric convolution and the discrete sine and cosine transforms”, IEEE Trans. Signal Process., 42 (1994), 1038–1051  crossref  adsnasa  isi
36. Vilenkin N. Ja., Klimyk A. U., Representations of Lie groups and special functions, Vol. 2, Kluwer, Dordrecht, 1993  mathscinet  zmath
37. Karlin S., McGregor J., “Determinants of orthogonal polynomials”, Bull. Amer. Math. Soc., 68 (1962), 204–209  crossref  mathscinet
38. Koornwinder T., “Two-variable analogues of the classical orthogonal polynomials”, Theory and Applications of Special Functions, ed. R. A. Askey, Academic Press, New York, 1975, 435–495  mathscinet
39. Berens H., Schmid H., Xu Y., “Multivariate Gaussian cubature formulas”, Arch. Math., 64 (1995), 26–32  crossref  mathscinet  zmath  isi

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