Generating Function for GLn-Invariant Differential Operators in the Skew Capelli Identity |
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Authors: | Takashi Hashimoto |
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Affiliation: | 1.Department of Informatics, Graduate School of Engineering,Tottori University,Tottori,Japan |
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Abstract: | Let Alt n be the vector space of all alternating n × n complex matrices, on which the complex general linear group GL n acts by ({x mapsto gxg^t}). The aim of this paper is to show that Pfaffian of a certain matrix whose entries are multiplication operators or derivations acting on polynomials on Alt n provides a generating function for the GL n -invariant differential operators that play an essential role in the skew Capelli identity, with coefficients the Hermite polynomials. |
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