TY - JOUR

T1 - Explicit Capelli identities for skew symmetric matrices

AU - Kinoshita, Kenji

AU - Wakayama, Masato

N1 - Funding Information:
Acknowledgements. The authors express their thanks to Hiroyuki Ochiai for making them aware of a gap in the proof of the main theorem in the first draft of the paper and Roger Howe for his helpful comments. M.W. was partly supported by grant-in-aid for Scientific Research (B) no. 09440022, from the Ministry of Education, Science and Culture of Japan.

PY - 2002

Y1 - 2002

N2 - 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 GLN. 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 GLN.

AB - 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 GLN. 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 GLN.

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U2 - 10.1017/S0013091500001176

DO - 10.1017/S0013091500001176

M3 - Article

AN - SCOPUS:0036307283

SN - 0013-0915

VL - 45

SP - 449

EP - 465

JO - Proceedings of the Edinburgh Mathematical Society

JF - Proceedings of the Edinburgh Mathematical Society

IS - 2

ER -