On the Siegel-Weil formula: The case of singular forms

被引：14

作者：

Yamana, Shunsuke ^{[1
]}

机构：

[1] Osaka City Univ, Grad Sch Sci, Dept Math, Sumiyoshi Ku, Osaka 5588585, Japan

来源：

COMPOSITIO MATHEMATICA | 2011年 / 147卷 / 04期

关键词：

Eisenstein series; Siegel-Weil formula; singular forms; DEGENERATE PRINCIPAL SERIES; LOCAL THETA CORRESPONDENCE; EISENSTEIN SERIES; UNITARY GROUPS; REPRESENTATIONS;

D O I：

10.1112/S0010437X11005379

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For the dual pair Sp(n) x O(m) with m <= n, we prove an identity between a special value of a certain Eisenstein series and the regularized integral of a theta function. The proof uses the functional equation of the Eisenstein series and the regularized Siegel-Weil formula for Sp(n) x O(2n + 2 - m). Analogous results for unitary and orthogonal groups are included.

引用

页码：1003 / 1021

页数：19

共 33 条

[1] Degenerate principal series representations of GLn(C) and GLn(R) [J].

Howe, R ;

Lee, ST .

JOURNAL OF FUNCTIONAL ANALYSIS, 1999, 166 (02) :244-309

[2] A regularized Siegel-Weil formula for unitary groups [J].

Ichino, A .

MATHEMATISCHE ZEITSCHRIFT, 2004, 247 (02) :241-277

[3]

Ichino A, 2001, J REINE ANGEW MATH, V539, P201

[4] On the Siegel-Weil formula for unitary groups [J].

Ichino, Atsushi .

MATHEMATISCHE ZEITSCHRIFT, 2007, 255 (04) :721-729

[5]

Ikeda T, 1996, COMPOS MATH, V103, P183

[6] On the genericity of cuspidal automorphic forms of SO(2n+1), II [J].

Jiang, Dihua ;

Soudry, David .

COMPOSITIO MATHEMATICA, 2007, 143 (03) :721-748

[7]

Kudla S. S., 2006, ANN MATH STUDIES, V161

[8]

Kudla S.S., 1990, ISRAEL MATH C P, P81

[9]

KUDLA SS, 1988, J REINE ANGEW MATH, V391, P65

[10] A REGULARIZED SIEGEL-WEIL FORMULA - THE 1ST TERM IDENTITY [J].

KUDLA, SS ;

RALLIS, S .

ANNALS OF MATHEMATICS, 1994, 140 (01) :1-80

← 1 2 3 4 →