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Zapiski Nauchnykh Seminarov POMI, 2020, Volume 494, Pages 23–47
(Mi znsl6981)
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Regular representation of the group $\mathrm{GL}(N,\mathbb{R})$: factorization, Casimir operators and Toda chain
N. M. Belousov, S. E. Derkachev St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
Abstract:
The note is devoted to a factorization formula for the matrix constructed from the generators of the group $\mathrm{GL}(N,\mathbb{R})$ in its regular representation. The factorization formula makes it possible to calculate these generators together with Casimir operators in the case of an arbitrary $N$, and it also clarifies a link between the group $\mathrm{GL}(N,\mathbb{R})$ and the quantum Toda chain.
Key words and phrases:
General linear group, regular representation, factorization of matrix with generators, Casimir operators, quantum Toda chain.
Received: 18.11.2020
Citation:
N. M. Belousov, S. E. Derkachev, “Regular representation of the group $\mathrm{GL}(N,\mathbb{R})$: factorization, Casimir operators and Toda chain”, Questions of quantum field theory and statistical physics. Part 27, Zap. Nauchn. Sem. POMI, 494, POMI, St. Petersburg, 2020, 23–47
Linking options:
https://www.mathnet.ru/eng/znsl6981 https://www.mathnet.ru/eng/znsl/v494/p23
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Statistics & downloads: |
Abstract page: | 141 | Full-text PDF : | 134 | References: | 20 |
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