Advanced Studies in Pure Mathematics

Remarks on the Capelli identities for reducible modules

Tôru Umeda

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Abstract

Inspired by the new type of Capelli identity associated with the regular representation of quaternions obtained by An Huang [6], we present a more basic type of Capelli identities for reducible modules of the matrix algebras. As a related subject in view of reducible modules, we also discuss the Capelli identities associated with group determinants, for which a precise formulation and an answer are given.

Article information

Source
Representation Theory, Special Functions and Painlevé Equations — RIMS 2015, H. Konno, H. Sakai, J. Shiraishi, T. Suzuki and Y. Yamada, eds. (Tokyo: Mathematical Society of Japan, 2018), 527-541

Dates
Received: 16 October 2015
Revised: 17 August 2016
First available in Project Euclid: 21 September 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1537499436

Digital Object Identifier
doi:10.2969/aspm/07610527

Mathematical Reviews number (MathSciNet)
MR3837932

Zentralblatt MATH identifier
07039313

Subjects
Primary: 17B35: Universal enveloping (super)algebras [See also 16S30] 13N10: Rings of differential operators and their modules [See also 16S32, 32C38]

Keywords
Capelli identity group determinant

Citation

Umeda, Tôru. Remarks on the Capelli identities for reducible modules. Representation Theory, Special Functions and Painlevé Equations — RIMS 2015, 527--541, Mathematical Society of Japan, Tokyo, Japan, 2018. doi:10.2969/aspm/07610527. https://projecteuclid.org/euclid.aspm/1537499436


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