Whittaker Modules over the N = 2 Super-BMS3 Algebra

Qingyan Wu , Shoulan Gao , Dong Liu

Frontiers of Mathematics ›› : 1 -14.

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Frontiers of Mathematics ›› : 1 -14. DOI: 10.1007/s11464-023-0104-z
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Whittaker Modules over the N = 2 Super-BMS3 Algebra

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Abstract

This paper focuses on the analysis of Whittaker modules and high-order Whittaker modules over the N = 2 super-BMS3 algebra. We provide a classification of Whittaker vectors and establish the necessary and sufficient conditions for Whittaker modules to be simple. Additionally, we study the simple quotient of the universal Whittaker module if it is not simple.

Keywords

Whittaker module / high order Whittaker module / supersymmetric extension / super-BMS3 algebra

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Qingyan Wu, Shoulan Gao, Dong Liu. Whittaker Modules over the N = 2 Super-BMS3 Algebra. Frontiers of Mathematics 1-14 DOI:10.1007/s11464-023-0104-z

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References

[1]

Adamović D, R, Zhao K. Whittaker modules for the affine Lie algebra A1(1). Adv. Math., 2016, 289: 438-479.

[2]

Arnal D, Pinczon G. On algebraically irreducible representation of the Lie algebra sl2. J. Math. Phys., 1974, 15(3): 350-359.

[3]

Bagci I, Christodoulopoulou K, Wiesner E. Whittaker categories and strongly typical Whittaker modules for Lie superalgebras. Comm. Algebra, 2014, 42(11): 4932-4947.

[4]

Banerjee N., Mitra A., Mukherjee D., Safari H.R., Supersymmetrization of deformed BMS algebras. Eur. Phys. J. C, 2023, 83: Art. No. 3

[5]

Barnich G., Donnay L., Matulich J., Troncoso R., Asymptotic symmetries and dynamics of three-dimensional flat supergravity. J. High Energy Phys., 2014, 2014: Art. No. 71

[6]

Batra P, Mazorchuk V. Blocks and modules for Whittaker pairs. J. Pure Appl. Algebra, 2011, 215(7): 1552-1568.

[7]

Bondi H, van der Burg MGJ, Metzner AWK. Gravitational waves in general relativity. VII. Waves from axisymmetric isolated systems. Proc. R. Soc. London, Ser. A, 1962, 269: 21-52.

[8]

Chen C-W. Whittaker modules for classical Lie superalgebras. Commun. Math. Phys., 2021, 388: 351-383.

[9]

Chen H., Dai X., Liu Y., and Su Y., A class of non-weight modules over the super-BMS3 algebra. 2023, arXiv:1911.09651

[10]

Chi L, Sun J, Yang H. Lie super-bialgebra structures on the N = 2 super-BMS3 algebra. Asian-Eur. J. Math., 2021, 14(6): 2150103.

[11]

Christodoulopoulou K. Whittaker modules for Heisenberg algebras and imaginary Whittaker modules for affine Lie algebras. J. Algebra, 2008, 320(7): 2871-2890.

[12]

Dilxat M, Chen L, Liu D. Classification of simple Harish–Chandra modules over the Ovsienko–Roger superalgebra. Proc. Roy. Soc. Edinburgh Sect. A, 2024, 154(2): 483-493.

[13]

Dilxat M, Gao S, Liu D. 2-Local superderivations on the super Virasoro algebra and the super W(2, 2) algebra. Comm. Algebra, 2021, 49(12): 5423-5434.

[14]

Dilxat M., Gao S., Liu D., Whittaker modules over the N = 1 super-BMS3 algebra. J. Algebra Appl., 2024, 23 (5): Paper No. 2450088, 16 pp.

[15]

Gaiotto D. Asymptotically free N = 2 theories and irregular conformal blocks. J. Phys. Conf. Ser., 2013, 462(1): 012014.

[16]

Gao S, Pei Y, Bai C. Some algebraic properties of the supersymmetric extension of GCA in 2d. J. Phys. A, 2014, 47(22): 225202.

[17]

Guo X, Lu R, Zhao K. Irreducible modules over the Virasoro algebra. Doc. Math., 2011, 16: 709-721.

[18]

Henkel M, Schott R, Stoimenov S, Unterberger J. On the dynamical symmetric algebra of ageing: Lie structure, representations and Appell systems. Quantum Probability and Infinite Dimensional Analysis, 2007, Hackensack, NJ: World Scientific, 233-240.

[19]

Kostant B. On Whittaker vectors and representation theory. Invent. Math., 1978, 48(2): 101-184.

[20]

Liu D, Pei Y, Xia L. Whittaker modules for the super-Virasoro algebras. J. Algebra Appl., 2019, 18(11): 1950211.

[21]

Liu D, Pei Y, Xia L. Simple restricted modules for Neveu–Schwarz algebra. J. Algebra, 2020, 546: 341-356.

[22]

Liu D., Pei Y., Xia L., Zhao K., Smooth modules over the N = 1 Bondi–Metzner–Sachs superalgebra. 2023, arXiv:2307.14608

[23]

R, Zhao K. Generalized oscillator representations of the twisted Heisenberg–Virasoro algebra. Algebr. Represent. Theory, 2020, 23(4): 1417-1442.

[24]

Mandal I. Supersymmetric extension of GCA in 2d. J. High Energy Phys., 2010, 11: 1-28.

[25]

Mazorchuk V, Zhao K. Simple Virasoro modules which are locally finite over a positive part. Selecta Math., 2014, 20: 839-854.

[26]

Ondrus M, Wiesner E. Whittaker modules for the Virasoro algebra. J. Algebra Appl., 2009, 8(3): 363-377.

[27]

Ondrus M, Wiesner E. Whittaker categories for the Virasoro algebra. Comm. Algebra, 2013, 41(10): 3910-3930.

[28]

Tan S, Wang Q, Xu C. On Whittaker modules for a Lie algebra arising from the 2-dimensional torus. Pacific J. Math., 2015, 273(1): 147-167.

[29]

Wang B. Whittaker modules for graded Lie algebras. Algebr. Represent. Theory, 2011, 14(4): 691-702.

[30]

Yanagida S. Whittaker vectors of the Virasoro algebra in terms of Jack symmetric polynomial. J. Algebra, 2011, 333(1): 273-294.

[31]

Zhang X, Tan S, Lian H. Whittaker modules for the Schrödinger–Witt algebra. J. Math. Phys., 2010, 51(8): 083524.

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