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Regular Representation of the Group GL(N, ℝ): Factorization, Casimir Operators and Toda Chain

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The note is devoted to the factorization formula for the matrix with the generators of the group GL(N, ℝ) in the regular representation. The factorization formula helps to evaluate these generators and Casimir operators in the case of arbitrary N and clarifies the connection between GL(N, ℝ) and the quantum Toda chain.

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Authors and Affiliations

  1. St.Petersburg Department of the Steklov Mathematical Institute, St. Petersburg, Russia

    N. Belousov & S. Derkachov

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  1. N. Belousov
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  2. S. Derkachov
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Correspondence to N. Belousov.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 494, 2020, pp. 23–47.

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Belousov, N., Derkachov, S. Regular Representation of the Group GL(N, ℝ): Factorization, Casimir Operators and Toda Chain. J Math Sci 264, 215–231 (2022). https://doi.org/10.1007/s10958-022-05993-8

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  • DOI: https://doi.org/10.1007/s10958-022-05993-8

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