# DEGENERATE PRINCIPAL SERIES FOR EXCEPTIONAL p-ADIC GROUPS OF TYPE G2

• Choi, Seun-Gil (DEPARTMENT OF INDUSTRIAL INFORMATION, COLLEGE OF INDUSTRIAL SCIENCES, KONGJU NATIONAL UNIVERSITY)
• Published : 2006.11.30

#### Abstract

We determine reducibility points of degenerate principal series for exceptional p-adic groups of type $G_2$ via Jacquet module techniques and Hecke algebra isomorphisms.

#### References

1. D. Ban and C. Jantzen, Degenerate Principal Series for even-orthogonal groups, Represent. Theory 7 (2003), 440–480 https://doi.org/10.1090/S1088-4165-03-00166-3
2. D. Barbasch, Reducibility of some spherical induced modules for $F_{4}$ (Note)
3. I. Bernstein and A. Zelevinsky, Induced representations of reductive p-adic groups. I., Ann. Sci. Ecole Norm. Sup. (4) 10 (1997), no. 4, 441–472
4. C. Bushnell and P. Kutzko, Smooth representations of reductive p-adic groups: structure theory via types, Proc. London Math. Soc. (3) 77 (1998), no. 3, 582-634
5. H. Jacquet, Representation des groupes lineaires p-adiques, Theory of group representations and Fourier Analysis, C. I. M. E. (1971), 119–220
6. C. Jantzen, Degenerate principal series for orthogonal groups, J. Reine Angew. Math. 441 (1993), 61–98
7. C. Jantzen, Degenerate principal series for symplectic groups, Mem. Amer. Math. Soc. 102 (1993), no. 488
8. C. Jantzen,, Degenerate principal series for symplectic and odd-orthogonal groups, Mem. Amer. Math. Soc. 124 (1996), no. 590
9. C. Jantzen and H. Kim, Parametrization of the image of normalized intertwining operators, Pacific J. Math. 199 (2001), no. 2, 367–415
10. G. Muic, The unitary dual of p-adic $G_{2}$, Duke Math. J. 90 (1997), no. 3, 465–493 https://doi.org/10.1215/S0012-7094-97-09012-8
11. A. Moy, Minimal K-types for $G_{2}$ over a p-adic field, Trans. Amer. Math. Soc. 305 (1988), no. 2, 517–529 https://doi.org/10.2307/2000877
12. A. Roche, Types and Hecke algebras for principal series representations of split reductive p-adic groups, Ann. Sci. Ecole Norm. Sup. (4) 31 (1998), no. 3, 361–413 https://doi.org/10.1016/S0012-9593(98)80139-0
13. M. Tadic, Notes on representations of non-archimedian SL(n), Pacific J. Math. 152 (1992), no. 2, 375–396 https://doi.org/10.2140/pjm.1992.152.375
14. M. Tadic, On reducibility of parabolic induction, Israel J. Math. 107 (1998), 29–91
15. A. V. Zelevinsky, Induced representations of reductive p-adic groups. II. On irreducible representations of GL(n), Ann. Sci. Ecole Norm. Sup. (4) 13 (1980), no. 2, 165–210 https://doi.org/10.24033/asens.1379