论文信息 - Conductors and newforms for non-supercuspidal representations of unramified U(2,1)

Conductors and newforms for non-supercuspidal representations of unramified U(2,1)

Let G be the unramified unitary group in three variables defined over a p-adic field with odd p. The conductors and newforms for representations of G are defined by using a certain family of open compact subgroups of G. In this paper, we determine the conductors of non-supercuspidal representations of G, and give explicit newforms in induced representations for non-supercuspidal generic representations.

Michitaka Miyauchi | M. Miyauchi

[1] REPRESENTATIONS OF THE GROUP GL(n, F) WHERE F IS A NON-ARCHIMEDEAN LOCAL FIELD , 1976 .

[2] Hervé Jacquet,et al. Conducteur des représentations du groupe linéaire , 1981 .

[3] B. Roberts,et al. Local newforms for GSp(4) , 2007 .

[4] Conductors and newforms for U(1,1) , 2004, math/0503090.

[5] Mark Reeder. OLD FORMS ON GLn , 1991 .

[6] On epsilon factors attached to supercuspidal representations of unramified U(2,1) , 2011, 1111.2212.

[7] M. Miyauchi. On local newforms for unramified U(2, 1) , 2011, 1105.6004.

[8] W. Casselman. On some results of Atkin and Lehner , 1973 .

[9] D. Keys. Principal series representations of special unitary groups over local fields , 1984 .

[10] A. Raghuram,et al. Conductors and newforms for SL(2) , 2007 .

[11] E. M. Baruch. On the gamma factors attached to representations ofU(2,1) over ap-adic field , 1997 .

[12] I. Piatetski-Shapiro,et al. Automorphic forms and L-functions for the unitary group , 1983 .