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Proceedings of the American Mathematical Society

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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
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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$.

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  • [G-Z] I. M. Gel'fand and A. V. Zelevinskii, Models of representations of classical groups and their hidden symmetries, Functional Anal. Appl. 18 (1984), 183-198. MR 757246 (86i:22024)
  • [P-SA] J. Pantoja et 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, C. R. Acad. Sci. Paris Sér. I. Math. 302 (1986), 463-466. MR 838400 (87e:22041)
  • [R] F. Rodier, Décomposition spectrale des représentations lisses, Non-commutative Harmonic Analysis (Marseille-Luminy 1976), Lecture Notes in Math., vol. 587, Springer-Verlag, Berlin and New York, 1977, pp. 177-195. MR 0460549 (57:542)
  • [S1] M. Saito, Représentations unitaires du groupe de déplacements du plan $ \mathfrak{p}$-adique, Proc. Japan Acad. 39 (1963), 407-409. MR 0166300 (29:3577)
  • [S2] -, Représentations unitaires du groupe des déplacements dans un plan $ \mathfrak{p}$-adique, J. Math. Soc. Japan 19 (1967), 411-425. MR 0220874 (36:3926)
  • [Sa] P. J. Sally, Jr., Invariant subspaces and Fourier-Bessel transforms on the $ \mathfrak{p}$-adic plane, Math. Ann. 174 (1967), 247-264. MR 0579179 (58:28317)
  • [V] N. Ya. Vilenkin, Special functions and the theory of group representations, Transl. Math. Monographs, vol. 22, Amer. Math. Soc., Providence, R. I., 1968. MR 0229863 (37:5429)

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Article copyright: © Copyright 1988 American Mathematical Society

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