Minimal 𝐾-types for 𝐺₂ over a 𝑝-adic field

Moy, Allen

doi:10.1090/S0002-9947-1988-0924768-X

Minimal $K$-types for $G_ 2$ over a $p$-adic field
HTML articles powered by AMS MathViewer

by Allen Moy

Trans. Amer. Math. Soc. 305 (1988), 517-529

DOI: https://doi.org/10.1090/S0002-9947-1988-0924768-X

PDF | Request permission

Abstract:

We single out certain representations of compact open subgroups of ${G_2}$ over a $p$-adic field and show they play a role in the representation theory of ${G_2}$ similar to minimal $K$-types in the theory of real groups.

References

Bomshik Chang, The conjugate classes of Chevalley groups of type $(G_{2})$, J. Algebra 9 (1968), 190–211. MR 227258, DOI 10.1016/0021-8693(68)90020-3
Harish-Chandra, Eisenstein series over finite fields, Functional Analysis and Related Fields (Proc. Conf. for M. Stone, Univ. Chicago, Chicago, Ill., 1968) Springer, New York, 1970, pp. 76–88. MR 0457579

Homomorphisms for

adic groups

Hecke algebra isomorphisms for

over a

adic field

Philip Kutzko and David Manderscheid, On the supercuspidal representations of $\textrm {GL}_4$. I, Duke Math. J. 52 (1985), no. 4, 841–867. MR 816388, DOI 10.1215/S0012-7094-85-05244-5
Allen Moy, Representations of $\textrm {U}(2,1)$ over a $p$-adic field, J. Reine Angew. Math. 372 (1986), 178–208. MR 863523, DOI 10.1515/crll.1986.372.178

Representations of

over a

adic field

Gopal Prasad and M. S. Raghunathan, Topological central extensions of semisimple groups over local fields, Ann. of Math. (2) 119 (1984), no. 1, 143–201. MR 736564, DOI 10.2307/2006967
George B. Seligman, On automorphisms of Lie algebras of classical type. II, Trans. Amer. Math. Soc. 94 (1960), 452–482. MR 113969, DOI 10.1090/S0002-9947-1960-0113969-9