W -Algebras via Lax Type Operators
197
23. F. Delduc, L. Fehér, Regular conjugacy classes in the Weyl group and integrable hierarchies. J.
Phys. A 28(20), 5843–5882 (1995)
24. V.G. Drinfeld, V.V. Sokolov, Lie algebras and equations of KdV type. Soviet J. Math. 30,
1975–2036 (1985)
25. V.A. Fateev, S.L. Lukyanov, The models of two-dimensional conformal quantum field theory
with Z n symmetry. Int. J. Mod. Phys. A 3(2), 507–520 (1988)
26. L. Fehér, J. Harnad, I. Marshall, Generalized Drinfeld-Sokolov reductions and KdV type
hierarchies. Commun. Math. Phys. 154(1), 181–214 (1993)
27. B.L. Feigin, E. Frenkel, Quantization of Drinfeld-Sokolov reduction. Phys. Lett. B 246, 75–81
(1990)
28. B.L. Feigin, E. Frenkel, Quantization of soliton systems and Langlands duality, in Exploring
New Structures and Natural Constructions in Mathematical Physics. Advanced Studies in Pure
Mathematics, vol. 61 (Mathematical Society Japan, Tokyo, 2011), pp. 185–274
29. C. Fernández-Pousa, M. Gallas, L. Miramontes, J. Sánchez Guillén, W-algebras from soliton
equations and Heisenberg subalgebras. Ann. Phys. 243(2), 372–419 (1995)
30. C. Fernández-Pousa, M. Gallas, L. Miramontes, J. Sánchez Guillén, Integrable Systems and
W-Algebras. VIII J. A. Swieca Summer School on Particles and Fields (Rio de Janeiro, 1995),
pp. 475–479
31. E. Frenkel, Affine algebras, Langlands duality and Bethe ansatz, in XIth International Congress
of Mathematical Physics (Paris, 1994) (International Press, Cambridge, 1995), pp. 606–642
32. E. Frenkel, T. Arakawa, Quantum Langlands duality of representations of W -algebras.
Compos. Math. 155(12), 2235–2262 (2019)
33. E. Frenkel, D. Hernandez, Spectra of quantum KdV Hamiltonians, Langlands duality, and
affine opers. Comm. Math. Phys. 362(2), 361–414 (2018)
34. W.L. Gan, V. Ginzburg, Quantization of Slodowy slices. Int. Math. Res. Not. 5, 243–255 (2002)
35. I.M. Gelfand, S.I. Gelfand, V. Retakh, R.I. Wilson, Quasideterminants. Adv. Math. 193(1),
56–141 (2005)
36. V.G. Kac, M. Wakimoto, Quantum reduction and representation theory of superconformal
algebras. Adv. Math. 185, 400–458 (2004). Corrigendum, Adv. Math. 193, 453–455 (2005)
37. V.G. Kac, M. Wakimoto, Quantum reduction in the twisted case. Progress Math. 237, 85–126
(2005)
38. V.G. Kac, S.-S. Roan, M. Wakimoto, Quantum reduction for affine superalgebras. Commun.
Math. Phys. 241, 307–342 (2003)
39. B. Kostant, On Whittaker vectors and representation theory. Inv. Math 48, 101–184 (1978)
40. S.L. Lukyanov, V.A. Fateev, Exactly soluble models of conformal quantum field theory
associated with the simple Lie algebra D n . Yadernaya Fiz. 49(5), 1491–1504 (1989)
41. T.E. Lynch, Generalized Whittaker vectors and representation theory, Thesis (Ph.D.), Massachusetts Institute of Technology, 1979
42. F. Magri, A simple model of the integrable Hamiltonian equation. J. Math. Phys. 19(5),
1156–1162 (1978)
43. H. Matumoto, Whittaker modules associated with highest weight modules. Duke Math. J. 60,
59–113 (1990)
44. T. Milanov, D. Lewanski, W-algebra constraints and topological recursion for A N -singularity
(with an appendix by Danilo Lewanski). Int. J. Math. 27(13), 1650110 (2016)
45. A. Molev, Yangians and Classical Lie Algebras. Mathematical Surveys and Monographs, vol.
143 (American Mathematical Society, Providence, 2007)
46. A. Premet, Special transverse slices and their enveloping algebras. Adv. Math. 170, 1–55
(2002)
47. A. Premet, Enveloping algebras of Slodowy slices and the Joseph ideal. J. Eur. Math. Soc.
(JEMS) 9(3), 487–543 (2007)
48. O. Schiffmann, E. Vasserot, Cherednik algebras, W -algebras and the equivariant cohomology
of the moduli space of instantons on A 2 . Publ. Math. Inst. Hautes Etudes Sci. 118, 213–342
(2013)
197
23. F. Delduc, L. Fehér, Regular conjugacy classes in the Weyl group and integrable hierarchies. J.
Phys. A 28(20), 5843–5882 (1995)
24. V.G. Drinfeld, V.V. Sokolov, Lie algebras and equations of KdV type. Soviet J. Math. 30,
1975–2036 (1985)
25. V.A. Fateev, S.L. Lukyanov, The models of two-dimensional conformal quantum field theory
with Z n symmetry. Int. J. Mod. Phys. A 3(2), 507–520 (1988)
26. L. Fehér, J. Harnad, I. Marshall, Generalized Drinfeld-Sokolov reductions and KdV type
hierarchies. Commun. Math. Phys. 154(1), 181–214 (1993)
27. B.L. Feigin, E. Frenkel, Quantization of Drinfeld-Sokolov reduction. Phys. Lett. B 246, 75–81
(1990)
28. B.L. Feigin, E. Frenkel, Quantization of soliton systems and Langlands duality, in Exploring
New Structures and Natural Constructions in Mathematical Physics. Advanced Studies in Pure
Mathematics, vol. 61 (Mathematical Society Japan, Tokyo, 2011), pp. 185–274
29. C. Fernández-Pousa, M. Gallas, L. Miramontes, J. Sánchez Guillén, W-algebras from soliton
equations and Heisenberg subalgebras. Ann. Phys. 243(2), 372–419 (1995)
30. C. Fernández-Pousa, M. Gallas, L. Miramontes, J. Sánchez Guillén, Integrable Systems and
W-Algebras. VIII J. A. Swieca Summer School on Particles and Fields (Rio de Janeiro, 1995),
pp. 475–479
31. E. Frenkel, Affine algebras, Langlands duality and Bethe ansatz, in XIth International Congress
of Mathematical Physics (Paris, 1994) (International Press, Cambridge, 1995), pp. 606–642
32. E. Frenkel, T. Arakawa, Quantum Langlands duality of representations of W -algebras.
Compos. Math. 155(12), 2235–2262 (2019)
33. E. Frenkel, D. Hernandez, Spectra of quantum KdV Hamiltonians, Langlands duality, and
affine opers. Comm. Math. Phys. 362(2), 361–414 (2018)
34. W.L. Gan, V. Ginzburg, Quantization of Slodowy slices. Int. Math. Res. Not. 5, 243–255 (2002)
35. I.M. Gelfand, S.I. Gelfand, V. Retakh, R.I. Wilson, Quasideterminants. Adv. Math. 193(1),
56–141 (2005)
36. V.G. Kac, M. Wakimoto, Quantum reduction and representation theory of superconformal
algebras. Adv. Math. 185, 400–458 (2004). Corrigendum, Adv. Math. 193, 453–455 (2005)
37. V.G. Kac, M. Wakimoto, Quantum reduction in the twisted case. Progress Math. 237, 85–126
(2005)
38. V.G. Kac, S.-S. Roan, M. Wakimoto, Quantum reduction for affine superalgebras. Commun.
Math. Phys. 241, 307–342 (2003)
39. B. Kostant, On Whittaker vectors and representation theory. Inv. Math 48, 101–184 (1978)
40. S.L. Lukyanov, V.A. Fateev, Exactly soluble models of conformal quantum field theory
associated with the simple Lie algebra D n . Yadernaya Fiz. 49(5), 1491–1504 (1989)
41. T.E. Lynch, Generalized Whittaker vectors and representation theory, Thesis (Ph.D.), Massachusetts Institute of Technology, 1979
42. F. Magri, A simple model of the integrable Hamiltonian equation. J. Math. Phys. 19(5),
1156–1162 (1978)
43. H. Matumoto, Whittaker modules associated with highest weight modules. Duke Math. J. 60,
59–113 (1990)
44. T. Milanov, D. Lewanski, W-algebra constraints and topological recursion for A N -singularity
(with an appendix by Danilo Lewanski). Int. J. Math. 27(13), 1650110 (2016)
45. A. Molev, Yangians and Classical Lie Algebras. Mathematical Surveys and Monographs, vol.
143 (American Mathematical Society, Providence, 2007)
46. A. Premet, Special transverse slices and their enveloping algebras. Adv. Math. 170, 1–55
(2002)
47. A. Premet, Enveloping algebras of Slodowy slices and the Joseph ideal. J. Eur. Math. Soc.
(JEMS) 9(3), 487–543 (2007)
48. O. Schiffmann, E. Vasserot, Cherednik algebras, W -algebras and the equivariant cohomology
of the moduli space of instantons on A 2 . Publ. Math. Inst. Hautes Etudes Sci. 118, 213–342
(2013)