Within the framework of the so called ultrasecond quantization a
four-dimensional matrix eigenvalue problem described in ref. [2]
(and considered, separately, for bosons and fermions) is noticed to
possess compact exact solutions.

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MR2431588 Golikov, D. S.; Maslov, V. P. On the exact solution of a four-row matrix corresponding to the variational equation for ultrasecond-quantized problems. (Russian) Mat. Zametki 83 (2008), no. 2, 305--309. 81Q05 (15A06 34C60)