Crystal bases, dilogarithm identities and torsion in algebraic 𝐾-theory

Frenkel, Edward ; Szenes, András

Journal of the American Mathematical Society, Tome 08 (1995) no. 3, pp. 629-664

Détail

DOI : 10.1090/S0894-0347-1995-1266736-4

Bibliographie

[1] Andrews, George E., Baxter, R. J., Forrester, P. J. Eight-vertex SOS model and generalized Rogers-Ramanujan-type identities J. Statist. Phys. 1984 193 266

[2] Beä­Linson, A. A. Higher regulators and values of 𝐿-functions of curves Funktsional. Anal. i Prilozhen. 1980 46 47

[3] Bloch, Spencer The dilogarithm and extensions of Lie algebras 1981 1 23

[4] Coleman, Robert F. Dilogarithms, regulators and 𝑝-adic 𝐿-functions Invent. Math. 1982 171 208

[5] Date, E., Jimbo, M., Kuniba, A., Miwa, T., Okado, M. One-dimensional configuration sums in vertex models and affine Lie algebra characters Lett. Math. Phys. 1989 69 77

[6] Sah, Chih Han Scissors congruences. I. The Gauss-Bonnet map Math. Scand. 1981

[7] Nahm, W., Recknagel, A., Terhoeven, M. Dilogarithm identities in conformal field theory Modern Phys. Lett. A 1993 1835 1847

[8] Frenkel, Edward, Szenes, Andrã¡S Dilogarithm identities, 𝑞-difference equations, and the Virasoro algebra Internat. Math. Res. Notices 1993 53 60

[9] Goncharov, A. B. Geometry of configurations, polylogarithms, and motivic cohomology Adv. Math. 1995 197 318

[10] Govindachar, Suresh Explicit weight two motivic cohomology complexes and algebraic 𝐾-theory 𝐾-Theory 1992 387 430

[11] Jimbo, Michio, Misra, Kailash C., Miwa, Tetsuji, Okado, Masato Combinatorics of representations of 𝑈_{𝑞}(̂𝔰𝔩(𝔫)) at 𝔮 Comm. Math. Phys. 1991 543 566

[12] Kac, Victor G., Wakimoto, Minoru Modular invariant representations of infinite-dimensional Lie algebras and superalgebras Proc. Nat. Acad. Sci. U.S.A. 1988 4956 4960

[13] Kang, Seok-Jin, Kashiwara, Masaki, Misra, Kailash C., Miwa, Tetsuji, Nakashima, Toshiki, Nakayashiki, Atsushi Affine crystals and vertex models 1992 449 484

[14] Kang, Seok-Jin, Kashiwara, Masaki, Misra, Kailash C., Miwa, Tetsuji, Nakashima, Toshiki, Nakayashiki, Atsushi Perfect crystals of quantum affine Lie algebras Duke Math. J. 1992 499 607

[15] Kashiwara, M. On crystal bases of the 𝑄-analogue of universal enveloping algebras Duke Math. J. 1991 465 516

[16] Kirillov, A. N., Reshetikhin, N. Yu. Exact solution of the 𝑋𝑋𝑍 Heisenberg model of spin 𝑆 Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 1985

[17] Kirillov, A. N. Identities for the Rogers dilogarithmic function connected with simple Lie algebras Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 1987

[18] Levine, Marc The indecomposable 𝐾₃ of fields Ann. Sci. École Norm. Sup. (4) 1989 255 344

[19] Lewin, Leonard Polylogarithms and associated functions 1981

[20] Lichtenbaum, Stephen Groups related to scissors-congruence groups 1989 151 157

[21] Lusztig, G. Canonical bases arising from quantized enveloping algebras J. Amer. Math. Soc. 1990 447 498

[22] Merkur′Ev, A. S., Suslin, A. A. The group 𝐾₃ for a field Izv. Akad. Nauk SSSR Ser. Mat. 1990 522 545

[23] Nahm, W., Recknagel, A., Terhoeven, M. Dilogarithm identities in conformal field theory Modern Phys. Lett. A 1993 1835 1847

[24] Parry, Walter, Sah, Chih-Han Third homology of 𝑆𝐿(2,𝑅) made discrete J. Pure Appl. Algebra 1983 181 209

[25] Ramakrishnan, Dinakar Regulators, algebraic cycles, and values of 𝐿-functions 1989 183 310

[26] Richmond, Bruce, Szekeres, George Some formulas related to dilogarithms, the zeta function and the Andrews-Gordon identities J. Austral. Math. Soc. Ser. A 1981 362 373

[27] Sah, Chih-Han Homology of classical Lie groups made discrete. III J. Pure Appl. Algebra 1989 269 312

[28] Weibel, Charles A. Mennicke-type symbols for relative 𝐾₂ 1984 451 464

[29] Zagier, Don Polylogarithms, Dedekind zeta functions and the algebraic 𝐾-theory of fields 1991 391 430