Simple weight modules with finite weight multiplicities over the Lie algebra of polynomial vector fields

References

[1] Y. Billig and V. Futorny, Classification of irreducible representations of Lie algebra of vector fields on a torus, J. reine angew. Math. 720 (2016), 199–216. 10.1515/crelle-2014-0059Search in Google Scholar

[2] A. Cavaness and D. Grantcharov, Bounded weight modules of the Lie algebra of vector fields on ℂ 2 , J. Algebra Appl. 16 (2017), no. 12, Article ID 1750236. 10.1142/S021949881750236XSearch in Google Scholar

[3] I. Dimitrov, O. Mathieu and I. Penkov, On the structure of weight modules, Trans. Amer. Math. Soc. 352 (2000), no. 6, 2857–2869. 10.1090/S0002-9947-00-02390-4Search in Google Scholar

[4] B. L. Feĭgin and D. B. Fuks, Homology of the Lie algebra of vector fields on the line, Funct. Anal. Appl. 14 (1980), 201–212. 10.1007/BF01086182Search in Google Scholar

[5] S. L. Fernando, Lie algebra modules with finite-dimensional weight spaces. I, Trans. Amer. Math. Soc. 322 (1990), no. 2, 757–781. 10.1090/S0002-9947-1990-1013330-8Search in Google Scholar

[6] D. B. Fuks, Cohomology of infinite-dimensional Lie algebras, Contemp. Sov. Math., Consultants Bureau, New York 1986. 10.1007/978-1-4684-8765-7Search in Google Scholar

[7] V. Futorny, The weight representations of semisimple finite-dimensional Lie algebras, Ph.D. thesis, Kiev University, 1987. Search in Google Scholar

[8] D. Grantcharov and V. Serganova, Category of 𝔰 ⁢ 𝔭 ⁢ ( 2 ⁢ n ) -modules with bounded weight multiplicities, Mosc. Math. J. 6 (2006), no. 1, 119–134, 222. 10.17323/1609-4514-2006-6-1-119-134Search in Google Scholar

[9] D. Grantcharov and V. Serganova, Cuspidal representations of 𝔰 ⁢ 𝔩 ⁢ ( n + 1 ) , Adv. Math. 224 (2010), no. 4, 1517–1547. 10.1016/j.aim.2009.12.024Search in Google Scholar

[10] D. Grantcharov and V. Serganova, On weight modules of algebras of twisted differential operators on the projective space, Transform. Groups 21 (2016), no. 1, 87–114. 10.1007/s00031-015-9344-7Search in Google Scholar

[11] T. A. Larsson, Conformal fields: A class of representations of V ⁢ e ⁢ c ⁢ t ⁢ ( N ) , Int. J. Modern Phys. A 7 (1992), no. 26, 6493–6508. 10.1142/S0217751X92002970Search in Google Scholar

[12] G. Liu, R. Lu and K. Zhao, Irreducible Witt modules from Weyl modules and 𝔤 ⁢ 𝔩 n -modules, J. Algebra 511 (2018), 164–181. 10.1016/j.jalgebra.2018.06.021Search in Google Scholar

[13] O. Mathieu, Classification of Harish-Chandra modules over the Virasoro Lie algebra, Invent. Math. 107 (1992), no. 2, 225–234. 10.1007/BF01231888Search in Google Scholar

[14] O. Mathieu, Classification of irreducible weight modules, Ann. Inst. Fourier (Grenoble) 50 (2000), no. 2, 537–592. 10.5802/aif.1765Search in Google Scholar

[15] I. Penkov and V. Serganova, Weight representations of the polynomial Cartan type Lie algebras W n and S ¯ n , Math. Res. Lett. 6 (1999), no. 3–4, 397–416. 10.4310/MRL.1999.v6.n4.a3Search in Google Scholar

[16] A. N. Rudakov, Irreducible representations of infinite-dimensional Lie algebras of Cartan type (Russian), Izv. Akad. Nauk SSSR Ser. Mat. 38 (1974), 835–866; translation in USSR-Izv. 8 (1974), 836–866. 10.1070/IM1974v008n04ABEH002129Search in Google Scholar

[17] A. N. Rudakov, Irreducible representations of infinite-dimensional Lie algebras of types S and H (Russian), Izv. Akad. Nauk SSSR Ser. Mat. 39 (1975), no. 3, 496–511; translation in USSR-Izv. 9 (1975), 465–480. Search in Google Scholar

[18] G. Y. Shen, Graded modules of graded Lie algebras of Cartan type. I. Mixed products of modules, Sci. Sinica Ser. A 29 (1986), no. 6, 570–581. Search in Google Scholar

[19] Y. Xue and R. Lu, Classification of simple bounded weight modules of the Lie algebra of vector fields on ℂ n , preprint (2020), https://arxiv.org/abs/2001.04204. Search in Google Scholar