A note on the Capelli identities for symmetric pairs of Hermitian type

被引：0

作者：

Nishiyama, Kyo ^{[1
]}

Wachi, Akihito ^{[2
]}

机构：

[1] Kyoto Univ, Dept Math, Grad Sch Sci, Sakyo Ku, Kyoto 6068502, Japan

[2] Hokkaido Inst Technol Maeda, Div Comprehens Educ, Teine Ku, Sapporo, Hokkaido 0068585, Japan

来源：

INFINITE DIMENSIONAL HARMONIC ANALYSIS IV: ON THE INTERPLAY BETWEEN REPRESENTATION THEORY, RANDOM MATRICES, SPECIAL FUNCTIONS, AND PROBABILITY | 2009年

关键词：

Capelli identity; symmetric space; invariant differential operators; dual pair; Weil representation; GENERALIZED VERMA MODULES; REDUCTIVE DUAL PAIRS; MATRICES;

D O I：

10.1142/9789812832825_0016

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We get several identities of differential operators in determinantal form. These identities are non-commutative versions of the formula of Cauchy-Binet or Laplace expansions of determinants, and if we take principal symbols, they are reduced to such classical formulas. These identities are naturally arising from the generators of the rings of invariant differential operators over symmetric spaces, and have strong resemblance to the classical Capelli identities. Thus we call those identities the Capelli identities for symmetric pairs.

引用

页码：223 / +

页数：3

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