The Plancherel transform on the nilpotent part of $G_{2}$ and some applocations to the representation theory of $G_{2}$
HTML articles powered by AMS MathViewer
- by Kenneth I. Gross PDF
- Trans. Amer. Math. Soc. 132 (1968), 411-446 Request permission
References
- Robert J. Blattner, On induced representations, Amer. J. Math. 83 (1961), 79–98. MR 125456, DOI 10.2307/2372722
- Robert J. Blattner, Positive definite measures, Proc. Amer. Math. Soc. 14 (1963), 423–428. MR 147580, DOI 10.1090/S0002-9939-1963-0147580-9 Séminaire Bourbaki, Analyse spectrale et théorème de prédiction statistique de Wiener, Exposé 218, Secrétariat Math., Paris, 1961.
- Claude Chevalley, Theory of Lie groups. I, Princeton University Press, Princeton, N. J., 1946 1957. MR 0082628, DOI 10.1515/9781400883851
- C. Chevalley, Sur certains groupes simples, Tohoku Math. J. (2) 7 (1955), 14–66 (French). MR 73602, DOI 10.2748/tmj/1178245104 Séminaire Chevalley, Classification des groupes de Lie algébriques, Secrétariat Math., Paris, 1958.
- J. Dixmier, Sur les représentations unitaires des groupes de Lie nilpotents. II, Bull. Soc. Math. France 85 (1957), 325–388 (French). MR 95426, DOI 10.24033/bsmf.1492
- Sigurđur Helgason, Differential geometry and symmetric spaces, Pure and Applied Mathematics, Vol. XII, Academic Press, New York-London, 1962. MR 0145455
- N. Jacobson, Cayley numbers and normal simple Lie algebras of type $\textrm {G}$, Duke Math. J. 5 (1939), 775–783. MR 598, DOI 10.1215/S0012-7094-39-00562-4
- N. Jacobson, Composition algebras and their automorphisms, Rend. Circ. Mat. Palermo (2) 7 (1958), 55–80. MR 101253, DOI 10.1007/BF02854388
- Nathan Jacobson, Lie algebras, Interscience Tracts in Pure and Applied Mathematics, No. 10, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0143793
- A. A. Kirillov, Unitary representations of nilpotent Lie groups, Uspehi Mat. Nauk 17 (1962), no. 4 (106), 57–110 (Russian). MR 0142001
- R. A. Kunze and E. M. Stein, Uniformly bounded representations. III. Intertwining operators for the principal series on semisimple groups, Amer. J. Math. 89 (1967), 385–442. MR 231943, DOI 10.2307/2373128
- George W. Mackey, Imprimitivity for representations of locally compact groups. I, Proc. Nat. Acad. Sci. U.S.A. 35 (1949), 537–545. MR 31489, DOI 10.1073/pnas.35.9.537
- M. A. Naĭmark, Normed rings, Reprinting of the revised English edition, Wolters-Noordhoff Publishing, Groningen, 1970. Translated from the first Russian edition by Leo F. Boron. MR 0355601
Additional Information
- © Copyright 1968 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 132 (1968), 411-446
- MSC: Primary 22.65
- DOI: https://doi.org/10.1090/S0002-9947-1968-0233933-6
- MathSciNet review: 0233933