Given a representation of a local unitary group and another local unitary group , either the Theta correspondence provides a representation of or we set . If is fixed and varies in a Witt tower, a natural question is: for which is ? For given dimension there are exactly two isometry classes of unitary spaces that we denote . For let us denote the minimal of the same parity of such that , then we prove that where is the dimension of .
Étant donnée une représentation d’un groupe unitaire local et un autre groupe unitaire local , on sait que soit la correspondance Theta fournit une représentation de soit on pose . Si on fixe et on laisse varier dans une tour de Witt, une question naturelle est : pour quels a-t-on ? Pour chaque dimension il y a exactement deux classes d’équivalence d’espaces unitaires que nous dénotons . Pour , dénotons le plus petit de la parité de tel que , alors nous montrons que où est la dimension de .
@article{AFST_2011_6_20_1_167_0, author = {Gong, Z. and Greni\'e, L.}, title = {An inequality for local unitary {Theta} correspondence}, journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques}, pages = {167--202}, publisher = {Universit\'e Paul Sabatier, Institut de math\'ematiques}, address = {Toulouse}, volume = {Ser. 6, 20}, number = {1}, year = {2011}, doi = {10.5802/afst.1289}, mrnumber = {2830396}, language = {en}, url = {http://www.numdam.org/articles/10.5802/afst.1289/} }
TY - JOUR AU - Gong, Z. AU - Grenié, L. TI - An inequality for local unitary Theta correspondence JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2011 SP - 167 EP - 202 VL - 20 IS - 1 PB - Université Paul Sabatier, Institut de mathématiques PP - Toulouse UR - http://www.numdam.org/articles/10.5802/afst.1289/ DO - 10.5802/afst.1289 LA - en ID - AFST_2011_6_20_1_167_0 ER -
%0 Journal Article %A Gong, Z. %A Grenié, L. %T An inequality for local unitary Theta correspondence %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2011 %P 167-202 %V 20 %N 1 %I Université Paul Sabatier, Institut de mathématiques %C Toulouse %U http://www.numdam.org/articles/10.5802/afst.1289/ %R 10.5802/afst.1289 %G en %F AFST_2011_6_20_1_167_0
Gong, Z.; Grenié, L. An inequality for local unitary Theta correspondence. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 20 (2011) no. 1, pp. 167-202. doi : 10.5802/afst.1289. http://www.numdam.org/articles/10.5802/afst.1289/
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