EXPLICIT CAPELLI IDENTITIES FOR SKEW SYMMETRIC MATRICES

Proceedings of the Edinburgh Mathematical Society

Kenji Kinoshita¹ 

[1] Masato Wakayama

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

DOI  :  10.1017/S0013091500001176

学科分类：数学（综合）

来源: Cambridge University Press

【 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 $GL_N$.AMS 2000 Mathematics subject classification: Primary 17B35. Secondary 17B10; 15A15; 20G05

【 授权许可】

Unknown