Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Structure of generalized local rigid motion groups


Authors: J. Pantoja and J. Soto-Andrade
Journal: Proc. Amer. Math. Soc. 104 (1988), 693-696
MSC: Primary 22E20; Secondary 20F99, 20G25, 22E50
MathSciNet review: 964844
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We consider the higher-order local field analogue of the real euclidean plane afforded by a Galois field extension of degree $ n$, and we describe the structure of its corresponding "rigid motion" group $ G$.


References [Enhancements On Off] (What's this?)

  • [G-Z] I. M. Gel′fand and A. V. Zelevinskiĭ, Models of representations of classical groups and their hidden symmetries, Funktsional. Anal. i Prilozhen. 18 (1984), no. 3, 14–31 (Russian). MR 757246
  • [P-SA] José Pantoja and Jorge Soto-Andrade, Fonctions sphériques et modèles de Gel′fand pour le groupe de mouvements rigides d’un espace para-euclidien sur un corps local, C. R. Acad. Sci. Paris Sér. I Math. 302 (1986), no. 13, 463–466 (French, with English summary). MR 838400
  • [R] François Rodier, Décomposition spectrale des représentations lisses, Non-commutative harmonic analysis (Actes Colloq., Marseille-Luminy, 1976), Springer, Berlin, 1977, pp. 177–195. Lecture Notes in Math., Vol. 587 (French). MR 0460549
  • [S1] Masahiko Saito, Représentations unitaires du groupe des déplacements du plan 𝔭-adique, Proc. Japan Acad. 39 (1963), 407–409 (French). MR 0166300
  • [S2] Masahiko Saito, Représentations unitaires du groupe des déplacements dans un plan 𝔭-adique, J. Math. Soc. Japan 19 (1967), 411–425 (French). MR 0220874
  • [Sa] Paul J. Sally Jr., Invariant subspaces and Fourier-Bessel transforms on the 𝔓-adic plane, Math. Ann. 174 (1967), 247–264. MR 0579179
  • [V] N. Ja. Vilenkin, Special functions and the theory of group representations, Translated from the Russian by V. N. Singh. Translations of Mathematical Monographs, Vol. 22, American Mathematical Society, Providence, R. I., 1968. MR 0229863

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 22E20, 20F99, 20G25, 22E50

Retrieve articles in all journals with MSC: 22E20, 20F99, 20G25, 22E50


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0964844-4
Article copyright: © Copyright 1988 American Mathematical Society