Whittaker modules for two families of Whittaker pairs related to the subalgebras of the Virasoro algebra generated by L r , . . . , L 2r and L 1 , L n are analyzed. The structure theorems for the corresponding universal Whittaker modules are proved and some of their consequences are derived. All the Gaiotto [e-print arXiv:0908.0307] and the Bonelli-Maruyoshi- Tanzini [J. High Energy Phys. 1202, 031 (2012)] states in an arbitrary Virasoro algebra Verma module are explicitly constructed. C 2012 American Institute of Physics. [http://dx.
A flow in the formulation and proof of Lemma 2.7 of E. Felińska, Z. Jaskólski, and M. M. Kosztołowicz, J. Math. Phys. 53, 033504 (2012) is fixed in Sec. I of this Erratum. This has no consequences for the rest of the paper. An essential error was made in Theorems 3.5, 3.6, and Corollary 3.7 of Sec. III of E. Felińska, Z. Jaskólski, and M. M. Kosztołowicz, J. Math. Phys. 53, 033504 (2012). As it was pointed out by V. Mazorchuk and K. Zhao [“Simple Virasoro modules which are locally finite over positive part,” e-print arXiv:1205.5937v2 [math.RT]] they are valid only in the very limited case of n = 3. In order to introduce necessary correction we have rewritten a part of Sec. III after Theorem 3.3. This is presented in Sec. II of this Erratum.
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