Kazhdan-Lusztig correspondence for the representation category of the triplet W-algebra in logarithmic CFT

D. Kazhdan and G. Lusztig, J. Am. Math. Soc., 6, 905, 949 (1993); 7, 335, 383 (1994).

M. Finkelberg, Geom. Funct. Anal., 6, 249 (1996); V. G. Turaev, Quantum Invariants of Knots and 3-Manifolds, de Gruyter, Berlin (1994).

G. Moore and N. Seiberg, “Lectures on RCFT,” in: Superstrings’89 (Proc. Spring School held in Trieste, Italy, April 3–14, 1989, M. Green, R. Iengo, S. Randjbar-Daemi, E. Sezgin, and A. Strominger, eds.), World Scientific, Singapore (1990), p. 263.

J. Fuchs, I. Runkel, and C. Schweigert, Nucl. Phys. B, 646, 353 (2002); hep-th/0204148 (2002).

E. Frenkel and D. Ben-Zvi, Vertex Algebras and Algebraic Curves (Math. Surv. Monographs, Vol. 88), Amer. Math. Soc., Providence, R. I. (2001); B. Bakalov and A. A. Kirillov, Lectures on Tensor Categories and Modular Functors, Amer. Math. Soc., Providence, R. I. (2001); J. Fuchs, I. Runkel, and C. Schweigert, Nucl. Phys. B, 678, 511 (2004); hep-th/0306164 (2003).

J. Fuchs, I. Runkel, and C. Schweigert, “Ribbon categories and (unoriented) CFT: Frobenius algebras, automorphisms, reversions,” math.CT/0511590 (2005).

M. Miyamoto, “A theory of tensor products for vertex operator algebra satisfying C 2-cofiniteness,” math.QA/0309350 (2003).

Y.-Z. Huang, J. Lepowsky, and L. Zhang, “A logarithmic generalization of tensor product theory for modules for a vertex operator algebra,” math.QA/0311235 (2003).

J. Fuchs, “On non-semisimple fusion rules and tensor categories,” hep-th/0602051 (2006).

H. G. Kausch, Phys. Lett. B, 259, 448 (1991).

B. L. Feigin, A. M. Gainutdinov, A. M. Semikhatov, and I. Yu. Tipunin, Comm. Math. Phys., 265, 47 (2006); hep-th/0504093 (2005).

J. Fuchs, S. Hwang, A. M. Semikhatov, and I. Yu. Tipunin, Comm. Math. Phys., 247, 713 (2004); hepth/0306274 (2003).

M. Auslander, I. Reiten, and S. O. Smalø, Representation Theory of Artin Algebras (Cambridge Studies Adv. Math., Vol. 36), Cambridge Univ. Press, Cambridge (1995).

M. A. I. Flohr, Internat. J. Mod. Phys. A, 11, 4147 (1996); hep-th/9509166 (1995).

T. Kerler and V. V. Lyubashenko, Non-Semisimple Topological Quantum Field Theories for 3-Manifolds with Corners (Lect. Notes Math., Vol. 1765), Springer, Berlin (2001).

M. Flohr and M. R. Gaberdiel, J. Phys. A, 39, 1955 (2006); hep-th/0509075 (2005).

V. Lyubashenko, Comm. Math. Phys., 172, 467 (1995); hep-th/9405167 (1994); “Modular properties of ribbon abelian categories,” in: Proc. 2nd Gauss Symposium, Conference A: Mathematical and Theoretical Physics (Munich, Germany, August 2–7, 1993, M. Behara, R. Fritsch, and R. G. Lintz, eds.), de Gruyter, Berlin (1995), p. 529; hep-th/9405168 (1994); J. Pure Appl. Algebra, 98, 279 (1995); V. Lyubashenko and S. Majid, J. Algebra, 166, 506 (1994).

M. R. Gaberdiel and H. G. Kausch, Nucl. Phys. B, 477, 293 (1996); hep-th/9604026 (1996).

S. MacLane, Homology, Springer, Berlin (1963).

W. Crawley-Boevey, “Lectures on representations of quivers,” Lectures at Oxford in 1992, available at http://www.amsta.leeds.ac.uk/∼pmtwc/.

H. G. Kausch, Nucl. Phys. B, 583, 513 (2000); hep-th/0003029 (2000).

M. R. Gaberdiel and H. G. Kausch, Phys. Lett. B, 386, 131 (1996); hep-th/9606050 (1996).

H. G. Kausch, “Curiosities at c = −2,” hep-th/9510149 (1995).

S. Arkhipov, R. Bezrukavnikov, and V. Ginzburg, J. Am. Math. Soc., 17, 595 (2004); math.RT/0304173 (2003).

Y.-Z. Huang and L. Kong, “Full field algebras,” math.QA/0511328 (2005).

P. Gabriel, Manuscripta Math., 6, 71 (1972); correction, 6, 309 (1972); J. Bernstein, I. Gel’fand, and V. Ponomarev, Russ. Math. Surveys, 28, No. 2, 17 (1973).

L. A. Nazarova, Math. USSR Izv., 7, 749 (1974); P. Donovan and M. R. Freislich, The Representation Theory of Finite Graphs and Associated Algebras (Carleton Math. Lect. Notes, No. 5), Carleton Univ. Press, Ottawa, Ont., Canada (1973).

V. Dlab and C. M. Ringel, Mem. Am. Math. Soc., 173, 1 (1976).

I. Frenkel, A. Malkin, and M. Vybornov, “Affine Lie algebras and tame quivers,” math.RT/0005119 (2000).

L. Kronecker, Sitzungsber. Akad. Berlin, 1890, 1225 (1890).