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Notes on $\widetilde{\mathrm{SL}}(2,\mathbb{R})$ representations · Around

2017

Notes on $\widetilde{\mathrm{SL}}(2,\mathbb{R})$ representations

Kitaev, Alexei

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These notes describe representations of the universal cover of $\mathrm{SL}(2,\mathbb{R})$ with a view toward applications in physics.

Spinors on the hyperbolic plane and the two-dimensional anti-de Sitter space are also discussed.

Built on

V. Bargmann, “Irreducible unitary representations of the Lorentz group”, Annals of Mathematics
1947
Earlier work this paper cites.
Harish-Chandra, “Plancherel formula for the 2 × 2 2\times 2 real unimodular group”, Proc. Natl. Acad. Sci. U.S.A
1952
Earlier work this paper cites.
L. Pukánszky, “The Plancherel formula for the universal covering group of SL ⁡ ( ℝ , 2 ) \mathrm{SL}(\mathbb{R},2) ”, Math. Annalen
1964
Earlier work this paper cites.

Similar

J. Repka, “Tensor products of unitary representations of SL 2 ( ℝ ) \mathrm{SL}_{2}(\mathbb{R}) ”, Bull. Am. Math. Soc
1976
Cited alongside, same era.
J. Repka, “Tensor products of unitary representations of SL 2 ( ℝ ) \mathrm{SL}_{2}(\mathbb{R}) ”, Am. J. Math
Original
1978
Cited alongside, same era.
S. Sachdev and J. Ye, “Gapless spin-fluid ground state in a random quantum Heisenberg magnet”, Phys. Rev. Lett
1993
Cited alongside, same era.

Then

A. Kitaev, “A simple model of quantum holography”, KITP talks, April 7 and May 27 , 2015
2015
Later among the works it cites.
J. Maldacena and D. Stanford, “Remarks on the Sachdev-Ye-Kitaev model”, Phys. Rev. D
Original
2016
Later among the works it cites.
A. Jevicki, K. Suzuki, J. Yoon, “Bi-local holography in the SYK model”, JHEP 2016
Original
2016
Later among the works it cites.

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