Explicit Capelli identities for skew symmetric matrices

被引：11

作者：

Kinoshita, K

Wakayama, M

机构：

[1] Atlas Informat Serv Co Ltd, Chuo Ku, Osaka 5410041, Japan

[2] Kyushu Univ, Dept Math, Fukuoka 8128581, Japan

来源：

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY | 2002年 / 45卷

关键词：

Capelli identity; skew Capelli element; Pfaffian; universal enveloping algebra; invariant differential operator; Young diagram;

D O I：

10.1017/S0013091500001176

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The main purpose of this paper is to obtain an explicit Capelli identity relating skew-symmetric matrices under the action of the general linear group GL(N). In particular, we give an explicit formula for the skew Capelli element in terms of the trace of powers of a matrix defined by the standard infinitesimal generators of GL(N).

引用

页码：449 / 465

页数：17

共 10 条

[1] [Anonymous], 1995, LINEAR MULTILINEAR A, DOI DOI 10.1080/03081089508818403
[2] Graham R.L., 1989, Concrete Mathematics
[3] THE CAPELLI IDENTITY, THE DOUBLE COMMUTANT THEOREM, AND MULTIPLICITY-FREE ACTIONS
HOWE, R
UMEDA, T
[J]. MATHEMATISCHE ANNALEN, 1991, 290 (03) : 565 - 619
[4] Howe R, 1992, Israel Math. Conf. Proc, V8, P1
[5] Explicit Newton's formulas for gIn
Itoh, M
[J]. JOURNAL OF ALGEBRA, 1998, 208 (02) : 687 - 697
[6] MACDONALD IG, 1995, SYMMETRIC FUNCTIONS
[7] Newton's formula for gln
Umeda, T
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1998, 126 (11) : 3169 - 3175
[8] Umeda T., 1998, AM MATH SOC TRANSL 2, V183, P51
[9] Weyl H., 1946, The Classical Groups, V2nd ed.
[10] [No title captured]

← 1 →