In this paper, we introduce a family of functors denoted as , which act on algebraic D-modules and produce modules over N = 2 superconformal algebras. We demonstrate that these functors preserve irreducibility for all values of b, except for explicitly outlined cases. Moreover, we establish the necessary and sufficient conditions for determining the natural isomorphism between two such functors. Our constructed functors recover specific irreducible modules over N = 2 superconformal algebras, including intermediate series and -free modules. Additionally, we show that our constructed functors yield several new irreducible modules for N = 2 superconformal algebras.
REFERENCES
1.
Adamović
, D.
, “Representations of the N = 2 superconformal vertex algebra
,” Int. Math. Res. Not.
1999
, 61
–79
.2.
Block
, R.
, “The irreducible representations of the Lie algebra sl(2) and of the Weyl algebra and of the Weyl algebra
,” Adv. Math.
39
, 69
–110
(1981
).3.
Chen
, H.
, Dai
, X.
, and Liu
, M.
, “A family of simple non-weight modules over the twisted N = 2 superconformal algebra
,” J. Pure Appl. Algebra
226
, 107030
(2022
).4.
Chen
, H.
, Dai
, X.
, Liu
, D.
, and Pei
, Y.
, “Irreducible modules for super-Virasoro algebras from algebraic D-modules
,” J. Pure Appl. Algebra
228
, 107512
(2024
).5.
Cai
, Y.
, Chen
, H.
, Guo
, X.
, Ma
, Y.
, and Zhu
, M.
, “A class of non-weight modules of (2) and Clebsch–Gordan type formulas
,” Forum Math.
33
, 743
–755
(2021
).6.
Cai
, Y.
, Liu
, D.
, and Lü
, R.
, “Classification of simple Harish–Chandra modules over the N = 1 Ramond algebra
,” J. Algebra
567
, 114
–127
(2021
).7.
Cai
, Y.
and Lü
, R.
, “Classification of simple Harish–Chandra modules over the Neveu–Schwarz algebra and its contact subalgebra
,” J. Pure. Appl. Algebra
226
, 106866
(2022
).8.
Cheng
, S.
and Wang
, W.
, “Lie subalgebras of differential operators on the super circle
,” Publ. Res. Inst. Math. Sci.
39
, 545
–600
(2003
).9.
Dobrev
, V. K.
, “Characters of the unitarizable highest weight modules over the N = 2 superconformal algebras
,” Phys. Lett. B
186
, 43
–51
(1987
).10.
Dijkgraaf
, R.
, Verlinde
, H.
, and Verlinde
, E.
, “Topological strings in d < 1
,” Nucl. Phys. B
352
, 59
–86
(1991
).11.
Fu
, J.
, Jiang
, Q.
, and Su
, Y.
, “Classification of modules of the intermediate series over Ramond N = 2 superconformal algebras
,” J. Math. Phys.
48
, 043508
(2007
).12.
Feigin
, B. L.
, Semikhatov
, A. M.
, and Tipunin
, I. Y.
, “Equivalence between chain categories of representations of affine sl(2) and N = 2 superconformal algebras
,” J. Math. Phys.
39
, 3865
–3905
(1998
).13.
Feigin
, B. L.
, Semikhatov
, A. M.
, Sirota
, V. A.
, and Tipunin
, I. Y.
, “Resolutions and characters of irreducible representations of the N = 2 superconformal algebra
,” Nucl. Phys. B
536
, 617
–656
(1998
).14.
Iohara
, K.
and Koga
, Y.
, “Representation theory of Neveu–Schwarz and remond algebras I: Verma modules
,” Adv. Math.
177
, 61
–69
(2003
).15.
Iohara
, K.
and Koga
, Y.
, “Representation theory of Neveu–Schwarz and Ramond algebras II: Fock modules
,” An. Inst. Fourier
53
, 1755
–1818
(2003
).16.
Iohara
, K.
and Koga
, Y.
, “Representation theory of N = 2 super Virasoro algebra: Twisted sector
,” J. Funct. Anal.
214
, 450
–518
(2004
).17.
Iohara
, K.
, “Modules de plus haut poids unitarisables sur la super-algèbre de Virasoro N = 2 tordue
,” An. Inst. Fourier
58
, 733
–754
(2008
).18.
Iohara
, K.
, “Unitarizable highest weight modules of the N = 2 super Virasoro algebras: Untwisted sectors
,” Lett. Math. Phys.
91
, 289
–305
(2010
).19.
Kazama
, Y.
and Suzuki
, H.
, “New N = 2 superconformal field theories and superstring compactification
,” Nucl. Phys. B
321
, 232
–268
(1989
).20.
Kac
, V. G.
, Wakimoto
, M.
, and Mos
, T.
, “Representations of superconformal algebras and mock theta functions
,” Trans. Moscow Math. Soc.
78
, 9
–74
(2017
).21.
Liu
, D.
, Pei
, Y.
, and Xia
, L.
, “Classification of simple modules with finite-dimensional weight spaces for the N = 2 Ramond algebra
,” Sci. Sin. Math.
53
(9
), 1181
–1194
(2023
).22.
Liu
, D.
, Pei
, Y.
, and Xia
, L.
, “Whittaker modules for the super-Virasoro algebras
,” J. Algebra Appl.
18
, 1950211
(2019
).23.
Liu
, D.
, Pei
, Y.
, and Xia
, L.
, “Simple restricted modules for Neveu–Schwarz algebra
,” J. Algebra
546
, 341
–356
(2020
).24.
Li
, J.
, Su
, Y.
, and Zhu
, L.
, “Classification of indecomposable modules of the intermediate series over the twisted N = 2 superconformal algebra
,” J. Math. Phys.
51
, 083513
(2010
).25.
Lü
, R.
, Guo
, X.
, and Zhao
, K.
, “Irreducible modules over the Virasoro algebra
,” Doc. Math.
16
, 709
–721
(2011
).26.
Lü
, R.
and Zhao
, K.
, “Irreducible Virasoro modules from irreducible Weyl modules
,” J. Algebra
414
, 271
–287
(2014
).27.
Lü
, R.
and Zhao
, K.
, “A family of simple weight modules over the Virasoro algebra
,” J. Algebra
479
, 437
–460
(2017
).28.
Nillson
, J.
, “Simple (V)-modules which are free over an abelian subalgebra
,” Forum Math.
35
, 1237
–1255
(2023
).29.
Sato
, R.
, “Modular invariant representations of the superconformal algebra
,” Int. Math. Res. Not.
2019
, 7659
–7690
.30.
Su
, Y.
, “Classification of Harish-Chandra modules over the super-Virasoro algebras
,” Commun. Algebra
23
, 3653
–3675
(1995
).31.
Schwimmer
, A.
and Seiberg
, N.
, “Comments on the N = 2, 3, 4 superconformal algebras in two dimensions
,” Phys. Lett. B
184
, 191
–196
(1987
).32.
Semikhatov
, A. M.
and Tipunin
, I. Y.
, “The structure of Verma modules over the N = 2 superconformal algebra
,” Commun. Math. Phys.
195
, 129
–173
(1998
).33.
Xie
, Q.
and Sun
, J.
, “Non-weight modules over N = 1 Lie superalgebras of block type
,” Forum Mathe
35
, 1279
(2023
).34.
Xue
, Y.
and Lü
, R.
, “Simple weight modules with finite-dimensional weight spaces over Witt superalgebras
,” J. Algebra
574
, 92
–116
(2021
).35.
Yang
, H.
, Yao
, Y.
, and Xia
, L.
, “A family of non-weight modules over the super-Virasoro algebras
,” J. Algebra
547
, 538
–555
(2020
).36.
Yang
, H.
, Yao
, Y.
, and Xia
, L.
, “On non-weight representations of the N = 2 superconformal algebras
,” J. Pure Appl. Algebra
225
, 106529
(2021
).© 2024 Author(s). Published under an exclusive license by AIP Publishing.
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