Parabolically induced unitary representations of the universal group $U(F)^+$ are $C_0$
DOI:
https://doi.org/10.7146/math.scand.a-114722Abstract
We prove that all parabolically induced unitary representations of the Burger-Mozes universal group $U(F)^{+}$, with $F$ being primitive, are $C_0$. This generalizes the same well-known result for the universal group $U(F)^{+}$, when $F$ is $2$-transitive.
References
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Bekka, B., de la Harpe, P., and Valette, A., Kazhdan's property (T), New Mathematical Monographs, vol. 11, Cambridge University Press, Cambridge, 2008. https://doi.org/10.1017/CBO9780511542749
Burger, M. and Mozes, S., Groups acting on trees: from local to global structure, Inst. Hautes Études Sci. Publ. Math. (2000), no. 92, 113–150 (2001).
Caprace, P.-E. and De Medts, T., Simple locally compact groups acting on trees and their germs of automorphisms, Transform. Groups 16 (2011), no. 2, 375–411. https://doi.org/10.1007/s00031-011-9131-z
Ciobotaru, C., Parabolically induced unitary representations of the universal group $U(f)^+$ are $C_0$, long version arXiv:1409.2245v2, 2014.
Ciobotaru, C., A unified proof of the Howe-Moore property, J. Lie Theory 25 (2015), no. 1, 65–89.
Ciobotaru, C., The relative Howe-Moore property for the universal group $U(f)^+$, eprint arXiv:1612.09427, 2016.
Cluckers, R., Cornulier, Y., Louvet, N., Tessera, R., and Valette, A., The Howe-Moore property for real and $p$-adic groups, Math. Scand. 109 (2011), no. 2, 201–224. https://doi.org/10.7146/math.scand.a-15185
Tits, J., Sur le groupe des automorphismes d'un arbre, in “Essays on topology and related topics (Mémoires dédiés à Georges de Rham)'', Springer, New York, 1970, pp. 188-211.
Bekka, B., de la Harpe, P., and Valette, A., Kazhdan's property (T), New Mathematical Monographs, vol. 11, Cambridge University Press, Cambridge, 2008. https://doi.org/10.1017/CBO9780511542749
Burger, M. and Mozes, S., Groups acting on trees: from local to global structure, Inst. Hautes Études Sci. Publ. Math. (2000), no. 92, 113–150 (2001).
Caprace, P.-E. and De Medts, T., Simple locally compact groups acting on trees and their germs of automorphisms, Transform. Groups 16 (2011), no. 2, 375–411. https://doi.org/10.1007/s00031-011-9131-z
Ciobotaru, C., Parabolically induced unitary representations of the universal group $U(f)^+$ are $C_0$, long version arXiv:1409.2245v2, 2014.
Ciobotaru, C., A unified proof of the Howe-Moore property, J. Lie Theory 25 (2015), no. 1, 65–89.
Ciobotaru, C., The relative Howe-Moore property for the universal group $U(f)^+$, eprint arXiv:1612.09427, 2016.
Cluckers, R., Cornulier, Y., Louvet, N., Tessera, R., and Valette, A., The Howe-Moore property for real and $p$-adic groups, Math. Scand. 109 (2011), no. 2, 201–224. https://doi.org/10.7146/math.scand.a-15185
Tits, J., Sur le groupe des automorphismes d'un arbre, in “Essays on topology and related topics (Mémoires dédiés à Georges de Rham)'', Springer, New York, 1970, pp. 188-211.
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Published
2019-08-29
How to Cite
Ciobotaru, C. (2019). Parabolically induced unitary representations of the universal group $U(F)^+$ are $C_0$. MATHEMATICA SCANDINAVICA, 125(1), 113–134. https://doi.org/10.7146/math.scand.a-114722
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