Copyright © 2012 José O. Araujo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

1. I. Bernstein, I. Gelfand, and S. Gelfand, “Models of representations of Lie groups,” Selecta Mathematica Sovietica, vol. 1, no. 2, pp. 121–132, 1981.
2. R. Adin, A. Postnikov, and Y. Roichman, “A Gelfand model for wreath products,” Israel Journal of Mathematics, vol. 179, pp. 381–402, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
3. J. O. Araujo, “A Gel'fand model for a Weyl group of type $B_n$,” Contributions to Algebra and Geometry, vol. 44, no. 2, pp. 359–373, 2003.
4. J. O. Araujo and J. L. Aguado, “A Gel'fand model for the symmetric group,” Communications in Algebra, vol. 29, no. 4, pp. 1841–1851, 2001. View at Publisher · View at Google Scholar
5. J. O. Araujo and J. J. Bigeón, “A Gelfand model for a Weyl group of type $D_n$ and the branching rules $D_n\hookrightarrow B_n$,” Journal of Algebra, vol. 294, no. 1, pp. 97–116, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
6. R. Baddeley, “Models and involution models for wreath products and certain Weyl groups,” Journal of the London Mathematical Society, vol. 44, no. 1, pp. 55–74, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
7. R. Howlett and C. Zworestine, On Klyachkos Model for the Representations of Finite Linear Groups, Springer, Berlin, Germany, 2000.
8. N. F. J. Inglis, Richardson, and J. Saxl, “An explicit model for the complex representations of $S_n$,” Archiv der Mathematik, vol. 54, no. 3, pp. 258–259, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
9. N. F. J. Inglis and J. Saxl, “An explicit model for the complex representations of the finite general linear groups,” Archiv der Mathematik, vol. 57, no. 5, pp. 424–431, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
10. A. A. Klyachko, “Models for the complex representations of the groups GL(n, q),” Matematicheskiĭ Sbornik, vol. 48, no. 2, pp. 365–379, 1984. View at Publisher · View at Google Scholar
11. V. Kodiyalam and D. N. Verma, “A natural representation model for symmetric groups,” 2006, http://arxiv.org/abs/math/0402216v1.
12. J. Pantoja and J. Soto-Andrade, “Fonctions sphériques et modèles de Gel'fand pour le groupe de mouvements rigides d'un espace para-euclidien sur un corps local,” Comptes Rendus des Séances de l'Académie des Sciences, vol. 302, no. 13, pp. 463–466, 1986.
13. P. D. Ryan, “Representations of Weyl groups of type B induced from centralisers of involutions,” Bulletin of the Australian Mathematical Society, vol. 44, no. 2, pp. 337–344, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
14. R. Baddeley, “Some multiplicity-free characters of finite groups,” [Ph.D. Thesis], Cambridge, UK, 1991.
15. C. R. Vinroot, “Involution models of finite Coxeter groups,” Journal of Group Theory, vol. 11, no. 3, pp. 333–340, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
16. E. Marberg, “Automorphisms and generalized involution models of finite complex reflection groups,” Journal of Algebra, vol. 334, no. 1, pp. 295–320, 2011. View at Publisher · View at Google Scholar
17. C. Chevalley, “Invariants of finite groups generated by reflections,” American Journal of Mathematics, vol. 77, pp. 778–782, 1955. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
18. G. C. Shephard and J. A. Todd, “Finite unitary reflection groups,” Canadian Journal of Mathematics, vol. 6, pp. 274–304, 1954. View at Zentralblatt MATH
19. R. Steinberg, “Invariants of finite reflection groups,” Canadian Journal of Mathematics, vol. 12, pp. 606–615, 1960. View at Zentralblatt MATH
20. I. G. Macdonald, “Some irreducible representations of Weyl groups,” The Bulletin of the London Mathematical Society, vol. 4, pp. 148–150, 1972. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
21. J. O. Araujo and J. L. Aguado, “Representations of finite groups on polynomial rings,” in Actas V Congreso de Matemáticas “Dr. Antonio A. R. Monteiro”, Universidad Nacional del Sur, Bahia Blanca, Argentina, 1999.
22. S. M. Garge and J. Oesterlé, “On Gelfand models for finite Coxeter groups,” Journal of Group Theory, vol. 13, no. 3, pp. 429–439, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
23. R. Steinberg, “A geometric approach to the representations of the full linear group over a Galois field,” Transactions of the American Mathematical Society, vol. 71, pp. 274–282, 1951. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
24. G. Lusztig, “Irreducible representations of finite classical groups,” Inventiones Mathematicae, vol. 43, no. 2, pp. 125–175, 1977. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
25. W. M. Beynon and G. Lusztig, “Some numerical results on the characters of exceptional Weyl groups,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 84, no. 3, pp. 417–426, 1978. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
26. D. Alvis and G. Lusztig, “The representations and generic degrees of the Hecke algebra of type $H_4$,” Journal fur die Reine und Angewandte Mathematik, vol. 336, pp. 201–212, 1982. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
27. J. E. Björk, Ring of Differential Operators, North-Holland, 1979.
28. D. Bessis, “Sur le corps de définition d'un groupe de réflexions complexe,” Communications in Algebra, vol. 25, no. 8, pp. 2703–2716, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH