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Polynomial quantization and overalgebra for hyperboloid of one sheet

Annotation

We show that the multiplication of symbols in polynomial quantization is exactly an action of an overalgebra on the space of these symbols

Keywords

quantization; representations; hyperboloids; Poisson transforms

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DOI

10.20310/1810-0198-2018-23-123-353-360

UDC

517.98

Pages

353-360

References

1. Molchanov V.F. Quantization on para-Hermitian symmetric spaces. Amer. Math. Soc. Transl., Ser. 2, 1996, vol. 175, pp. 81-95. 2. Molchanov V.F., Volotova N.B. Polynomial quantization on rank one para-Hermitian symmetric spaces. Acta Appl. Math., 2004, vol. 81, no. 1-3, pp. 215-232. 3. Molchanov V.F. Berezin quantization as a part of the representation theory. Vestnik Tambovskogo universiteta. Seriya Estestvennye i tekhnicheskie nauki – Tambov University Reports. Series: Natural and Technical Sciences, 2017, vol. 22, no. 6, pp. 1235-1246. DOI: 10.20310/1810-0198-2017-22-6-1235-1246. 4. Neretin Yu.A. Deystvie nadalgebry v plansherelevskom razlozhenii i operatory sdviga v mnimom napravlenii [The action of an overalgebra in the Plancherel decomposition and shift operators in an imaginary direction]. Izvestiya Rossiyskoy akademii nauk. Seriya matematicheskaya – Izvestiya: Mathematics, 2002, vol. 66, no. 5, pp. 171-182. (In Russian). 5. Molchanov V.F. Canonical representations and overgroups. Amer. Math. Soc. Transl., Ser. 2, 2003, vol. 210, pp. 213-224. 6. Molchanov V.F. Canonical representations for hyperboloids: an interaction with an overalgebra. Geometric Methods in Physics. Bialowieza, 2016, pp. 129-138.

Received

2018-04-23

Section of issue

Scientific articles

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