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    Caracciolo, Sergio Sokal, Alan D. and Sportiello, Andrea 2013. Algebraic/combinatorial proofs of Cayley-type identities for derivatives of determinants and pfaffians. Advances in Applied Mathematics, Vol. 50, Issue. 4, p. 474.


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    Matsumoto, Sho 2005. α-Pfaffian, pfaffian point process and shifted Schur measure. Linear Algebra and its Applications, Vol. 403, p. 369.


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  • Proceedings of the Edinburgh Mathematical Society, Volume 45, Issue 2
  • June 2002, pp. 449-465

EXPLICIT CAPELLI IDENTITIES FOR SKEW SYMMETRIC MATRICES

  • Kenji Kinoshita (a1) and Masato Wakayama (a2)
  • DOI: http://dx.doi.org/10.1017/S0013091500001176
  • Published online: 01 June 2002
Abstract
Abstract

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

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Proceedings of the Edinburgh Mathematical Society
  • ISSN: 0013-0915
  • EISSN: 1464-3839
  • URL: /core/journals/proceedings-of-the-edinburgh-mathematical-society
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