Geodesic
Branching Rules for Ramified Principal Series Representations of GL(3) over a p-adic Field
Canadian journal of mathematics, Tome 62 (2010) no. 1, pp. 34-51

Voir la notice de l'article provenant de la source Cambridge University Press

We decompose the restriction of ramified principal series representations of the $p$ -adic group $\text{GL}\left( 3,\,\text{k} \right)$ to its maximal compact subgroup $K\,=\,\text{GL}\left( 3,\,\mathcal{R} \right)$ . Its decomposition is dependent on the degree of ramification of the inducing characters and can be characterized in terms of filtrations of the Iwahori subgroup in $K$ . We establish several irreducibility results and illustrate the decomposition with some examples.
DOI : 10.4153/CJM-2010-003-5
Mots-clés : principal series representations, branching rules, maximal compact subgroups, representations of p-adic groups 
Campbell, Peter S.; Nevins, Monica. Branching Rules for Ramified Principal Series Representations of GL(3) over a p-adic Field. Canadian journal of mathematics, Tome 62 (2010) no. 1, pp. 34-51. doi: 10.4153/CJM-2010-003-5
@article{10_4153_CJM_2010_003_5,
     author = {Campbell, Peter S. and Nevins, Monica},
     title = {Branching {Rules} for {Ramified} {Principal} {Series} {Representations} of {GL(3)} over a p-adic {Field}},
     journal = {Canadian journal of mathematics},
     pages = {34--51},
     year = {2010},
     volume = {62},
     number = {1},
     doi = {10.4153/CJM-2010-003-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2010-003-5/}
}
TY  - JOUR
AU  - Campbell, Peter S.
AU  - Nevins, Monica
TI  - Branching Rules for Ramified Principal Series Representations of GL(3) over a p-adic Field
JO  - Canadian journal of mathematics
PY  - 2010
SP  - 34
EP  - 51
VL  - 62
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2010-003-5/
DO  - 10.4153/CJM-2010-003-5
ID  - 10_4153_CJM_2010_003_5
ER  - 
%0 Journal Article
%A Campbell, Peter S.
%A Nevins, Monica
%T Branching Rules for Ramified Principal Series Representations of GL(3) over a p-adic Field
%J Canadian journal of mathematics
%D 2010
%P 34-51
%V 62
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-2010-003-5/
%R 10.4153/CJM-2010-003-5
%F 10_4153_CJM_2010_003_5

[BO] [BO] U., Bader and U., Onn, On some geometric representations of GLn(O). arXiv:math/0404408v1. Google Scholar

[CN] [CN] P. S., Campbell and M., Nevins, Branching rules for unramified principal series representations of GL(3) over a p-adic field. J. Algebra 321(2009), no. 9, 2422-2444. doi:10.1016/j.jalgebra.2009.01.013 Google Scholar

[GAP] [GAP] The GAP Group, GAP - Groups, Algorithms, and Programming. Version 4.4, 2004. http://www.gap-system.org. Google Scholar

[Hi] [Hi] G., Hill, On the nilpotent representations of GLn(O).Manuscripta Math. 82(1994), no. 3-4, 293-311. doi:10.1007/BF02567703 Google Scholar

[H1] [H1] R. E., Howe, On the principal series of GLn over p-adic fields. Trans. Amer.Math. Soc. 177(1973), 275-286. doi:10.2307/1996596 Google Scholar

[H2] [H2] R. E., Howe, Kirillov theory for compact p-adic groups. Pacific J. Math. 73(1977), no. 2, 365-381. Google Scholar

[L] [L] G., Lusztig, Representations of reductive groups over finite rings. Represent. Theory 8(2004), 1-14. doi:10.1090/S1088-4165-04-00232-8 Google Scholar

[N] [N] M., Nevins, Branching rules for principal series representations of SL(2 over a p-adic field. Canad. J. Math. 57(2005), no. 3, 648-672. Google Scholar

[OPV] [OPV] U., Onn, A., Prasad, and L., Vaserstein, A note on Bruhat decomposition of GL(n) over local principal ideal rings. Comm. Algebra 34(2006), no. 11, 4119-4130. doi:10.1080/00927870600876250 Google Scholar

[P] [P] V., Paskunas, Unicity of types for supercuspidal representations of GLN. >Proc. London Math. Soc. 91(2005), no. 3, 623-654. doi:10.1112/S0024611505015340 Proc.+London+Math.+Soc.+91(2005),+no.+3,+623-654.+doi:10.1112/S0024611505015340>Google Scholar

[Si] [Si] A. J., Silberger, Irreducible representations of a maximal compact subgroup of pgl2 over the p-adics. Math. Ann. 229(1977), no. 1, 1-12. doi:10.1007/BF01420533 Google Scholar

Cité par Sources :