[1] D. Adamovi´c and A. Milas, “On the triplet vertex algebra W (p)”, Advances in
Mathematics 217 (2008), 2664-2699.
[2] D. Adamovi´c and A. Milas, “The N = 1 triplet vertex operator superalgebras”,
Communications in Mathematical Physics, 288 (2009), 225-270.
[3] D. Adamovi´c and A. Milas, “Lattice construction of logarithmic modules for certain
vertex algebras”, Selecta Math. (N.S.) 15 (2009), 535-561; arXiv:0902.3417.
[4] D. Adamovi´c and A. Milas, “On W-algebras associated to (2, p) minimal models for
certain vertex algebras”, International Mathematics Research Notices 2010 (2010)
20 : 3896-3934, arXiv:0908.4053.
[5] D. Adamovi´c and A. Milas, “On W-algebra extensions of (2, p) minimal models: p
>3”, Journal of Algebra 344 (2011) 313-332. arXiv:1101.0803.
[6] D. Adamovi´c and A. Milas, “The structure of Zhu ’s algebras for certain Walgebras”, Advances in Math 227 (2011) 2425-2456; arXiv:1006.5134.
[7] D. Adamovi´c and A. Milas, “An explicit realization of logarithmic modules for the
vertex operator algebra Wp+ ,p− ”, J. Math. Phys. 53, (2012), 16pp.
[8] R. Allen and S. Wood, “Bosonic ghostbusting: the bosonic ghost vertex algebra
admits a logarithmic module category with rigid fusion”, Communications in Mathematical Physics, 390(2), 959-1015 (2022).
[9] Y. Arike, “A matrix realization of the quantum group gp,q ”, International Journal
of Mathematics, 22.03 (2011): 345-398.
[10] A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov, “Infinite conformal symmetry in two-dimensional quantum field theory”, Nuclear Physics B, 241(2), 333-380
(1984).
[11] O. Blondeau-Fournier, P. Mathieu, D. Ridout, and S. Wood, “Superconformal minimal models and admissible Jack polynomials”, Advances in Mathematics 314, 71123.
[12] B. Boe, D. Nakano and E. Wiesner, “Category O for the Virasoro algebra: cohomology and Koszulity”, Pacific J. Math. 234 (2008), no. 1, 1-21.
[13] M. Canagasabey, J. Rasmussen and D. Ridout, “Fusion rules for the N = 1 superconformal logarithmic minimal models I: The Neveu-Schwarz sector”, J. Phys.,
A48:415402, 2015. arXiv:1504.03155 [hep-th].
[14] T. Creutzig, S. Kanade, and R. McRae, “Tensor categories for vertex operator
superalgebra extensions”, arXiv:1705.05017 (2017).
[15] T. Creutzig, R. McRae. and J. Yang, “On ribbon categories for singlet
vertex algebras”, Communications in Mathematical Physics, 387(2), 865-925,
arXiv:2007.12735.
145
[16] T. Creutzig and D. Ridout. “Logarithmic conformal field theory: Beyond an introduction”, J. Phys. A46: 494006, 2013. arXiv:1303.0847 [hep-th].
[17] V. S. Dotsenko and V. A. Fateev, “Conformal algebra and multipoint correlation
functions in 2D statistical models”, Nuclear Phys. B 240 (1984), 312-348.
[18] V. S. Dotsenko and V. A. Fateev, “Four-point correlation functions and the operator
algebra in 2D conformal invariant theories with central charge c ≤ 1”, Nuclear Phys.
B 251 (1985), 691-734.
[19] NIST Digital Library of Mathematical Functions, Release 1.0.27 of 2020- 06-15, F.
Olver, A. Olde Daalhuis, D. Lozier, B. Schneider, R. Boisvert, C. Clark, B. Miller,
B. Saunders, H. Cohl and M. McClain, eds, http://dlmf.nist.gov/.
[20] P. Etingof, G. Shlomo, D. Nikshych, and V. Ostrik. Tensor Categories. Number
volume 205 in Mathematical Surveys and Monographs. American Mathematical
Society, 2015.
[21] B. Feigin and D.B. Fuchs. “Representations of the Virasoro algebra”, in Representations of infinite-dimensional Lie groups and Lie algebras, Gordon andd Breach,
New York (1989).
[22] B. L. Feigin, A.M. Gainutdinov, A.M. Semikhatov, and I. Yu Tipunin, “Logarithmic
extensions of minimal models: characters and modular transformation”, Nuclear
Phys. B 757(2006),303-343.
[23] B.L. Feigin, A.M. Gainutdinov, A.M. Semikhatov, and I. Yu Tipunin, “KazhdanLusztig-dual quantum group for logarithmic extensions of Virasoro minimal models”, J. Math. Phys. 48:032303, 2007.
[24] B. L. Feigin, A.M. Gainutdinov, A.M. Semikhatov, and I. Yu Tipunin, “Modular
group representations and fusion in logarithmic conformal field theories and in the
quantum group center”, Comm. Math. Phys. 265 (2006), 4793.
[25] B. L. Feigin, A.M. Gainutdinov, A.M. Semikhatov, and I. Yu Tipunin, “KazhdanLusztig correspondence for the representation category of the triplet W-algebra in
logarithmic CFT”, Theor. Math. Phys. 148 (2006) 1210-1235; Teor. Mat. Fiz. 148
(2006) 398-427.
[26] G. Felder, “BRST approach to minimal models”, Nuc. Phy. B 317 (1989) 215-236.
[27] J. Fjelstad, J. Fuchs, S. Hwang, A. M. Semikhatov, and I. Yu. Tipunin, “Logarithmic
conformal field theories via logarithmic deformation”, Nuclear Phys. B 633, 379-413
(2002).
[28] P. J. Forrester, Log-gases and random matrices (LMS-34), Princeton University
Press, 2010.
[29] E. Frenkel and D. Ben-Zvi, Vertex Algebras and Algebraic Curves, Mathematical
Surveys and Monographs, Amer. Math. Soc. 88 (2001).
146
[30] I. Frenkel, J. Lepowsky, and A. Meurman, Vertex operator algebras and the Monster,
Academic press (1989).
[31] M. R. Gaberdiel and H.G. Kausch, “Indecomposable fusion products”, Nucl. Phys.
B 477 (1996) 293 [hep-th/9604026].
[32] M. Gaberdiel, I. Runkel, and S. Wood, “Fusion rules and boundary conditions in
the c = 0 triplet model”, J.Phys. A42 (2009) 325403, arXiv:0905.0916 [hep-th].
[33] M. Gaberdiel, I. Runkel, and S. Wood, “A modular invariant bulk theory for the
c = 0 triplet model”, J.Phys. A:math. Theor. 44 (2011) 015204, arXiv:1008.0082v1.
[34] T. Gannon and C. Negron, “Quantum SL(2) and logarithmic vertex operator algebras at (p, 1)-central charge”, (2021) arXiv:2104.12821.
[35] M. Gorelik and V. Kac, “On complete reducibility for infinite-dimensional Lie algebras”, Adv. Math. 226 (2011), no. 2, 1911-1972.
[36] Y. Z. Huang, “Cofiniteness conditions, projective covers and the logarithmic tensor
product theory”, J. Pure Appl. Algebra, 213(4):458-475, 2009.
[37] Y. Z. Huang, J. Lepowsky, and L. Zhang, “Logarithmic tensor category theory
for generalized modules for a conformal vertex algebra, I: Introduction and strongly
graded algebras and their generalized modules”, Conformal Field Theories and Tensor Categories, 169-248, Math. Lect. Peking Univ., Springer, Heidelberg, 2014.
[38] Y. Z. Huang, J. Lepowsky, and L. Zhang, “Logarithmic tensor category theory for
generalized modules for a conformal vertex algebra, II: Logarithmic formal calculus
and properties of logarithmic intertwining operators”, arXiv:1012.4196.
[39] Y. Z. Huang, J. Lepowsky, and L. Zhang, “Logarithmic tensor category theory
for generalized modules for a conformal vertex algebra, III: Intertwining maps and
tensor product bifunctors”, arXiv:1012.4197.
[40] Y. Z. Huang, J. Lepowsky, and L. Zhang, “Logarithmic tensor category theory for
generalized modules for a conformal vertex algebra, IV: Constructions of tensor
product bifunctors and the compatibility conditions”, arXiv:1012.4198.
[41] Y. Z. Huang, J. Lepowsky, and L. Zhang, “Logarithmic tensor category theory for
generalized modules for a conformal vertex algebra, V: Convergence condition for
intertwining maps and the corresponding compatibility condition”, arXiv:1012.4199.
[42] Y. Z. Huang, J. Lepowsky, and L. Zhang, “Logarithmic tensor category theory for
generalized modules for a conformal vertex algebra, VI: Expansion condition, associativity of logarithmic intertwining operators, and the associativity isomorphisms”,
arXiv:1012.4202.
[43] Y. Z. Huang, J. Lepowsky, and L. Zhang, “Logarithmic tensor category theory for
generalized modules for a conformal vertex algebra, VII: Convergence and extension
properties and applications to expansion for intertwining maps”, arXiv:1110.1929.
147
[44] Y. Z. Huang, J. Lepowsky, and L. Zhang, “Logarithmic tensor category theory
for generalized modules for a conformal vertex algebra, VIII: Braided tensor category structure on categories of generalized modules for a conformal vertex algebra”,
arXiv:1110.1931.
[45] Y. Z. Huang and A. Milas, “Intertwining operator superalgebras and vertex tensor categories for superconformal algebras, I”, Communications in Contemporary
Mathematics, 4(02), 327-355 (2002).
[46] K. Iohara and Y. Koga, “Representation theory of Neveu-Schwarz and Ramond
algebras I: Verma modules”, Adv. Math., 178 (2003), 1-65.
[47] K. Iohara and Y.Koga, “Representation theory of Neveu-Schwarz and Ramond Algebra II: Fock modules”, Ann. Inst. Fourier, Grenoble, 53, 6 (2003), 1755-1818.
[48] K. Iohara and Y. Koga, Representation Theory of the Virasoro Algebra, Springer
Monographs in Mathematics, Berlin, Springer 2011.
[49] V. Kac and W. Wang, “Vertex Operator Superalgebras and Their”, Mathematical
aspects of conformal and topological field theories and quantum groups, 175, 161
(1994).
[50] V. G. Kac, Vertex algebras for beginners, No. 10. American Mathematical Soc.,
1998.
[51] S. Kanade and D. Ridout, “NGK and HLZ: Fusion for physicists and mathematicians”, In D Adamovic and P Papi, editors, Affine, Vertex and W-algebras, volume
37 of Springer INdAM, pages 135-181, Cham, 2019. Springer. arXiv:1812.10713
[math-ph].
[52] H. G. Kausch, “Extended conformal algebras generated by multiplet of primary
fields”, Phys. Lett. B, 259 (1991), 448-455.
[53] D. Kazhdan and G. Lusztig, “Tensor structures arising from affine Lie algebras.
IV”, Journal of the American Mathematical Society, 7(2) (1994), 383-453.
[54] J. K¨
ulshammer, “Representation type and Auslander-Reiten theory of FrobeniusLusztig kernels”, Ph.D. thesis, Christian-Albrechts-Universit¨at zu Kiel, 2012.
[55] K. Kyt¨ol¨a and D. Ridout, “On staggered indecomposable Virasoro modules”, J.
Math. Phys. 50 (2009) 123503, arXiv:0905.0108[math-ph].
[56] R. McRae and J. Yang, “Structure of Virasoro tensor categories at central charge
13 − 6p − 6p−1 for integers p > 1”, arXiv:2011.02170.
[57] A. Milas, “Fusion rings for degenerate minimal models”, J. Algebra 254 (2002), no.
2, 300-335.
[58] K. Nagatomo and A. Tsuchiya, “The Triplet Vertex Operator Algebra W (p) and
Restricted Quantum Group at Root of Unity”, Adv. Stdu. in Pure Math., Exploring
new Structures and Natural Constructions in Mathematical Physics, Amer. Math.
Soc. 61 (2011) 149, arXiv:0902.4607.
148
[59] L. Xianzu, “Fusion rules of Virasoro vertex operator algebras”, Proceedings of the
American Mathematical Society 143.9 (2015):3765-3776.
[60] J. Rasmussen, “W-extended logarithmic minimal models”, Nucl. Phys. B 807
(2009) 495 [0805.2991 [hep-th]].
[61] D. Ridout and S. Wood, “Modular transformations and Verlinde formulae for logarithmic (p+ , p− )-models”, Nuclear Physics B 880 (2014): 175-202.
[62] E. Sussman, “The singularities of Selberg-and Dotsenko-Fateev-like integrals”, 2022
(preprint).
[63] A. Tsuchiya and Y. Kanie, “Fock space representations of the Virasoro algebra Intertwining operators”, Publ. RIMS, Kyoto Univ. 22(1986) 259-327.
[64] A. Tsuchiya and S. Wood, “The tensor structure on the representation category of
the Wp triplet algebra”, J. Phys. A 46 (2013), no. 44, 445203, 40 pp.
[65] A. Tsuchiya and S. Wood, “On the extended W-algebra of type sl2 at positive
rational level” International Mathematics Research Notices, Volume 2015, Issue 14,
1 January 2015, Pages 5357-5435.
[66] S. Wood, “Fusion Rules of the Wp,q Triplet Models”, J. Phys. A 43 (2010) 045212.
[67] S. Yanagida. “Norm of logarithmic primary of Virasoro algebra”, Letters in Mathematical Physics 98.2 (2011): 133-156.
[68] Y. Zhu, “Modular invariance of characters of of vertex operator algebras”, J. Amer.
Math. Soc. 9 (1996), 237-302.
149
...