[1] Adamovi´c, D., Milas, A.: Vertex operator algebras associated to modular invariant represen.1/
tations for A1 . Math. Res. Lett. 2, 563–575 (1995) Zbl 0848.17033 MR 1359963
[2] Arakawa, T.: Representation theory of W -algebras. Invent. Math. 169, 219–320 (2007)
Zbl 1172.17019 MR 2318558
[3] Arakawa, T.: Representation theory of W -algebras, II. In: Exploring New Structures and Natural Constructions in Mathematical Physics, Adv. Stud. Pure Math. 61, Math. Soc. Japan,
Tokyo, 51–90 (2011) Zbl 1262.17014 MR 2867144
[4] Arakawa, T.: A remark on the C2 -cofiniteness condition on vertex algebras. Math. Z. 270,
559–575 (2012) Zbl 1351.17031 MR 2875849
[5] Arakawa, T.: Rationality of Bershadsky–Polyakov vertex algebras. Comm. Math. Phys. 323,
627–633 (2013) Zbl 1319.17015 MR 3096533
[6] Arakawa, T.: Associated varieties of modules over Kac–Moody algebras and C2 -cofiniteness
of W -algebras. Int. Math. Res. Notices 2015, 11605–11666 Zbl 1335.17011 MR 3456698
[7] Arakawa, T.: Rationality of W -algebras: principal nilpotent cases. Ann. of Math. (2) 182,
565–604 (2015) Zbl 1394.17058 MR 3418525
[8] Arakawa, T.: Rationality of admissible affine vertex algebras in the category O. Duke Math.
J. 165, 67–93 (2016) Zbl 1395.17057 MR 3450742
[9] Arakawa, T.: Chiral algebras of class and Moore–Tachikawa symplectic varieties.
arXiv:1811.01577 (2018)
[10] Arakawa, T., Creutzig, T., Feigin, B.: Urod algebras and translation of W-algebras. Forum
Math. Sigma, to appear; arXiv:2010.02427
[11] Arakawa, T., van Ekeren, J., Moreau, A.: Singularities of nilpotent Slodowy slices and collapsing levels of W-algebras. arXiv:2102.13462 (2021)
[12] Arakawa, T., Frenkel, E.: Quantum Langlands duality of representations of W -algebras. Compos. Math. 155, 2235–2262 (2019) Zbl 1475.17041 MR 4016057
[13] Arakawa, T., Futorny, V., Ramirez, L. E.: Weight representations of admissible affine vertex
algebras. Comm. Math. Phys. 353, 1151–1178 (2017) Zbl 1406.17037 MR 3652486
Rationality of W-algebras
2811
[14] Arakawa, T., Kuwabara, T., Malikov, F.: Localization of affine W-algebras. Comm. Math.
Phys. 335, 143–182 (2015) Zbl 1393.17040 MR 3314502
[15] Arakawa, T., Molev, A.: Explicit generators in rectangular affine W -algebras of type A. Lett.
Math. Phys. 107, 47–59 (2017) Zbl 1415.17027 MR 3598875
[16] Arakawa, T., Moreau, A.: Joseph ideals and lisse minimal W -algebras. J. Inst. Math. Jussieu
17, 397–417 (2018) Zbl 1416.17014 MR 3773273
[17] Arakawa, T., van Ekeren, J.: Modularity of relatively rational vertex algebras and fusion rules
of principal affine W -algebras. Comm. Math. Phys. 370, 205–247 (2019) Zbl 1429.17027
MR 3982694
[18] Beem, C., Lemos, M., Liendo, P., Peelaers, W., Rastelli, L., van Rees, B. C.: Infinite chiral
symmetry in four dimensions. Comm. Math. Phys. 336, 1359–1433 (2015) Zbl 1320.81076
MR 3324147
[19] Beem, C., Peelaers, W., Rastelli, L., van Rees, B. C.: Chiral algebras of class . J. High Energy
Phys. 2015, art. 20, 68 pp. (2015) Zbl 1388.81766 MR 3359377
[20] Boyarchenko, S. I., Levendorski˘ı, S. Z.: On affine Yangians. Lett. Math. Phys. 32, 269–274
(1994) Zbl 0834.17012 MR 1310291
[21] Brundan, J., Kleshchev, A.: Representations of shifted Yangians and finite W -algebras. Mem.
Amer. Math. Soc. 196, no. 918, viii+107 pp. (2008) Zbl 1169.17009 MR 2456464
[22] Collingwood, D. H., McGovern, W. M.: Nilpotent Orbits in Semisimple Lie Algebras. Van
Nostrand Reinhold, New York (1993) Zbl 0972.17008 MR 1251060
[23] Creutzig, T.: W-algebras for Argyres–Douglas theories. Eur. J. Math. 3, 659–690 (2017)
Zbl 1422.17026 MR 3687436
[24] Creutzig, T.: Fusion categories for affine vertex algebras at admissible levels. Selecta Math.
(N.S.) 25, art. 27, 21 pp. (2019) Zbl 1472.17089 MR 3932636
[25] Creutzig, T., Gaiotto, D.: Vertex algebras for S-duality. Comm. Math. Phys. 379, 785–845
(2020) Zbl 1481.17041 MR 4163353
[26] Creutzig, T., Huang, Y.-Z., Yang, J.: Braided tensor categories of admissible modules for affine
Lie algebras. Comm. Math. Phys. 362, 827–854 (2018) Zbl 1427.17038 MR 3845289
[27] Creutzig, T., Linshaw, A. R.: Cosets of the W k .sl4 ; fsubreg /-algebra. In: Vertex Algebras and
Geometry, Contemp. Math. 711, Amer. Math. Soc., Providence, RI, 105–117 (2018)
Zbl 1437.17014 MR 3831569
[28] Creutzig, T., Linshaw, A.: Trialities of W-algebras. Trans. Amer. Math. Soc. 369, 467–494
(2017) Zbl 1395.17062
[29] D’Andrea, A., De Concini, C., De Sole, A., Heluani, R., Kac, V.: Three equivalent definitions
of finite W -algebras. Appendix to [30] (2006)
[30] De Sole, A., Kac, V. G.: Finite vs affine W -algebras. Jpn. J. Math. 1, 137–261 (2006)
Zbl 1161.17015 MR 2261064
[31] Dedushenko, M., Gukov, S., Nakajima, H., Pei, D., Ye, K.: 3d TQFTs from Argyres–Douglas
theories. J. Phys. A 53, art. 43LT01, 12 pp. (2020) MR 4177061
[32] Di Francesco, P., Mathieu, P., Sénéchal, D.: Conformal Field Theory. Grad. Texts in Contemp.
Phys., Springer, New York (1997) Zbl 0869.53052 MR 1424041
[33] Dong, C., Jiao, X., Xu, F.: Quantum dimensions and quantum Galois theory. Trans. Amer.
Math. Soc. 365, 6441–6469 (2013) Zbl 1337.17018 MR 3105758
[34] Dong, C., Li, H., Mason, G.: Modular-invariance of trace functions in orbifold theory and
generalized Moonshine. Comm. Math. Phys. 214, 1–56 (2000) Zbl 1061.17025
MR 1794264
[35] Dong, C., Mason, G.: Rational vertex operator algebras and the effective central charge. Int.
Math. Res. Notices 2004, 2989–3008 Zbl 1106.17032 MR 2097833
[36] Duflo, M.: Sur la classification des idéaux primitifs dans l’algèbre enveloppante d’une algèbre
de Lie semi-simple. Ann. of Math. (2) 105, 107–120 (1977) Zbl 0346.17011 MR 430005
T. Arakawa, J. van Ekeren
2812
[37] Elashvili, A. G., Kac, V. G.: Classification of good gradings of simple Lie algebras. In: Lie
Groups and Invariant Theory, Amer. Math. Soc. Transl. (2) 213, Amer. Math. Soc., Providence, RI, 85–104 (2005) Zbl 1073.17002 MR 2140715
[38] Elashvili, A. G., Kac, V. G., Vinberg, E. B.: On exceptional nilpotents in semisimple Lie
algebras. J. Lie Theory 19, 371–390 (2009) Zbl 1252.17006 MR 2572134
[39] Feigin, B., Frenkel, E.: Quantization of the Drinfel0 d–Sokolov reduction. Phys. Lett. B 246,
75–81 (1990) Zbl 1242.17023 MR 1071340
[40] Feigin, B., Gukov, S.: VOAŒM4 . J. Math. Phys. 61, art. 012302, 27 pp. (2020)
Zbl 1478.17025 MR 4047476
.2/
[41] Feigin, B. L., Semikhatov, A. M.: Wn algebras. Nuclear Phys. B 698, 409–449 (2004)
Zbl 1123.17302 MR 2092705
[42] Fredrickson, L., Pei, D., Yan, W., Ye, K.: Argyres–Douglas theories, chiral algebras and wild
Hitchin characters. J. High Energy Phys. 2018, art. 150, 62 pp. Zbl 1384.81099
MR 3762496
[43] Frenkel, E.: Langlands Correspondence for Loop Groups. Cambridge Stud. Adv. Math. 103,
Cambridge Univ. Press, Cambridge (2007) Zbl 1133.22009 MR 2332156
[44] Frenkel, E., Kac, V., Wakimoto, M.: Characters and fusion rules for W -algebras via quantized
Drinfeld–Sokolov reduction. Comm. Math. Phys. 147, 295–328 (1992) Zbl 0768.17008
MR 1174415
[45] Frenkel, I. B., Huang, Y.-Z., Lepowsky, J.: On axiomatic approaches to vertex operator
algebras and modules. Mem. Amer. Math. Soc. 104, no. 494, viii+64 pp. (1993)
Zbl 0789.17022 MR 1142494
[46] Frenkel, I. B., Zhu, Y.: Vertex operator algebras associated to representations of affine and
Virasoro algebras. Duke Math. J. 66, 123–168 (1992) Zbl 0848.17032 MR 1159433
[47] Gaiotto, D., Rapˇcák, M.: Vertex algebras at the corner. J. High Energy Phys. 2019, art. 160,
85 pp. Zbl 1409.81148 MR 3919335
[48] Gaitsgory, D.: Quantum Langlands correspondence. arXiv:1601.05279 (2016)
[49] Genra, N.: Screening operators for W -algebras. Selecta Math. (N.S.) 23, 2157–2202 (2017)
Zbl 1407.17033 MR 3663604
[50] Ginzburg, V.: Harish-Chandra bimodules for quantized Slodowy slices. Represent. Theory 13,
236–271 (2009) Zbl 1250.17007 MR 2515934
[51] Gorelik, M., Kac, V.: On complete reducibility for infinite-dimensional Lie algebras. Adv.
Math. 226, 1911–1972 (2011) Zbl 1225.17026 MR 2737804
[52] Guay, N., Nakajima, H., Wendlandt, C.: Coproduct for Yangians of affine Kac–Moody
algebras. Adv. Math. 338, 865–911 (2018) Zbl 1447.17012 MR 3861718
[53] Huang, Y.-Z.: Rigidity and modularity of vertex tensor categories. Comm. Contemp. Math.
10, 871–911 (2008) Zbl 1169.17019 MR 2468370
[54] Huang, Y.-Z.: Vertex operator algebras and the Verlinde conjecture. Comm. Contemp. Math.
10, 103–154 (2008) Zbl 1180.17008 MR 2387861
[55] Huang, Y.-Z., Lepowsky, J.: A theory of tensor products for module categories for a vertex
operator algebra. I, II. Selecta Math. (N.S.) 1, 699–756, 757–786 (1995) Zbl 0854.17033
MR 1383584
[56] Humphreys, J. E.: Representations of Semisimple Lie Algebras in the BGG category O. Grad.
Stud. Math. 94, Amer. Math. Soc., Providence, RI (2008) Zbl 1177.17001 MR 2428237
[57] Jantzen, J. C.: Kontravariante Formen auf induzierten Darstellungen halbeinfacher LieAlgebren. Math. Ann. 226, 53–65 (1977) Zbl 0372.17003 MR 439902
[58] Joseph, A.: Gelfand–Kirillov dimension for the annihilators of simple quotients of Verma
modules. J. London Math. Soc. (2) 18, 50–60 (1978) Zbl 0401.17007 MR 506500
[59] Joseph, A.: Dixmier’s problem for Verma and principal series submodules. J. London Math.
Soc. (2) 20, 193–204 (1979) Zbl 0421.17005 MR 551445
Rationality of W-algebras
2813
[60] Joseph, A.: On the associated variety of a primitive ideal. J. Algebra 93, 509–523 (1985)
Zbl 0594.17009 MR 786766
[61] Kac, V.: Introduction to vertex algebras, Poisson vertex algebras, and integrable Hamiltonian
PDE. In: Perspectives in Lie Theory, Springer INdAM Ser. 19, Springer, 3–72 (2017)
Zbl 1430.17088 MR 3751122
[62] Kac, V., Roan, S.-S., Wakimoto, M.: Quantum reduction for affine superalgebras. Comm.
Math. Phys. 241, 307–342 (2003) Zbl 1106.17026 MR 2013802
[63] Kac, V. G., Peterson, D. H.: Infinite-dimensional Lie algebras, theta functions and modular
forms. Adv. Math. 53, 125–264 (1984) Zbl 0584.17007 MR 750341
[64] Kac, V. G., Wakimoto, M.: Modular invariant representations of infinite-dimensional Lie
algebras and superalgebras. Proc. Nat. Acad. Sci. U.S.A. 85, 4956–4960 (1988)
Zbl 0652.17010 MR 949675
[65] Kac, V. G., Wakimoto, M.: Classification of modular invariant representations of affine
algebras. In: Infinite-Dimensional Lie Algebras and Groups (Luminy-Marseille, 1988), Adv.
Ser. Math. Phys. 7, World Sci., Teaneck, NJ, 138–177 (1989) Zbl 0742.17022 MR 1026952
[66] Kac, V. G., Wakimoto, M.: On rationality of W -algebras. Transform. Groups 13, 671–713
(2008) Zbl 1221.17033 MR 2452611
[67] Li, H. S.: Symmetric invariant bilinear forms on vertex operator algebras. J. Pure Appl.
Algebra 96, 279–297 (1994) Zbl 0813.17020 MR 1303287
[68] Losev, I.: Finite-dimensional representations of W -algebras. Duke Math. J. 159, 99–143
(2011) Zbl 1235.17007 MR 2817650
[69] Matsuo, A., Nagatomo, K., Tsuchiya, A.: Quasi-finite algebras graded by Hamiltonian and
vertex operator algebras. In: Moonshine: the First Quarter Century and Beyond, London Math.
Soc. Lecture Note Ser. 372, Cambridge Univ. Press, Cambridge, 282–329 (2010)
Zbl 1227.17013 MR 2681785
[70] Matumoto, H.: Whittaker modules associated with highest weight modules. Duke Math. J. 60,
59–113 (1990) Zbl 0716.17007 MR 1047117
[71] Matumoto, H.: Correction to: “Whittaker modules associated with highest weight modules”.
Duke Math. J. 61, 973 (1990) Zbl 0716.17007 MR 1084467
[72] Premet, A.: Special transverse slices and their enveloping algebras. Adv. Math. 170, 1–55
(2002) Zbl 1005.17007 MR 1929302
[73] Premet, A.: Enveloping algebras of Slodowy slices and the Joseph ideal. J. Eur. Math. Soc. 9,
487–543 (2007) Zbl 1134.17307 MR 2314105
[74] Song, J., Xie, D., Yan, W.: Vertex operator algebras of Argyres–Douglas theories from M5branes. J. High Energy Phys. 2017, art. 123, 36 pp. Zbl 1383.81170 MR 3756667
[75] Ueda, M.: Affine super Yangians and rectangular W -superalgebras. J. Math. Phys. 63, art.
051701, 34 pp. (2022) Zbl 07464294 MR 4414365
[76] Van Ekeren, J.: Modular invariance for twisted modules over a vertex operator superalgebra.
Comm. Math. Phys. 322, 333–371 (2013) Zbl 1382.17016 MR 3077918
[77] Wang, Y., Xie, D.: Codimension-two defects and Argyres–Douglas theories from outerautomorphism twist in 6D .2; 0/ theories. Phys. Rev. D 100, art. 025001, 24 pp. (2019)
MR 4016843
[78] Xie, D., Yan, W.: Schur sector of Argyres–Douglas theory and W -algebra. SciPost Phys. 10,
art. 080, 35 pp. (2021) MR 4237774
[79] Xie, D., Yan, W., Yau, S.-T.: Chiral algebra of the Argyres–Douglas theory from M5 branes.
Phys. Rev. D 103, art. 065003, 6 pp. (2021) MR 4247563
[80] Yamauchi, H.: Extended Griess algebras and Matsuo–Norton trace formulae. In: Conformal Field Theory, Automorphic Forms and Related Topics, Contrib. Math. Comput. Sci. 8,
Springer, Heidelberg, 75–107 (2014) Zbl 1344.17025 MR 3559202
[81] Zhu, Y.: Modular invariance of characters of vertex operator algebras. J. Amer. Math. Soc. 9,
237–302 (1996) Zbl 0854.17034 MR 1317233
...