Tomoki Nakanishi
Professor
Graduate School of Mathematics
Nagoya University
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List of Pulicatications
Last updated on 2024/7/28
Statement (2012/2/2): Since 2008, I maintain the position of not publishing, not refereeing, and not doing editorial work in any Elsevier journal unless they radically change how they operate.
For the background, see
http://thecostofknowledge.com/ (The Cost of Knowledge)
http://gowers.wordpress.com/2012/01/21/elsevier-my-part-in-its-downfall/ (Gowers's Weblog on 2012/1/21).

Monographs in English


[2] Tomoki Nakanishi,
Cluster algebras and dilogarithm identities,
arXiv:2407.06668, 204 pp.

[1] Tomoki Nakanishi,
Cluster algebras and scattering diagrams,
MSJ Mem. 41 (2023), 279 pp; ISBN:978-4-86497-105-8.
Preface and contents (2023/2/3)
Part I. Basics in cluster algebras, arXiv:2201.11371, v3:85 pp. (2023/2/3)
Part II. Cluster patterns and scattering diagrams, arXiv:2103.16309, v5:89 pp. (2023/2/3)
Part III. Cluster scattering diagrams, arXiv:2111.00800, v6:110 pp. (2023/2/3)
Correction (2024/7/28)

Ariticles in English

(in the order of appearance in arXiv after 1992)

[56] Tomoki Nakanishi,
Pentagon relation in quantum cluster scattering diagrams,
arXiv:2202.01588, 33 pp.

[55] Feiyang Lin, Gregg Musiker, Tomoki Nakanishi,
Two formulas for \(F\)-polynomials,
Int. Math. Res. Not. 2024 (2024) 613--634; DOI:10.1093/imrn/rnad074.
arXiv:2112.11839, 15 pp.

[54] Tomoki Nakanishi,
Dilogarithm identities in cluster scattering diagrams,
Nagoya Math. J. 253 (2024) 1--22; DOI:10.1017/nmj.2023.15
arXiv:2111.09555, 20 pp.

[53] Tomoki Nakanishi,
Synchronicity phenomenon in cluster patterns,
J. London Math. Soc. 103 (2021) 1120--1152; DOI:10.1112/jlms.12402.
arXiv:1906.12036, 39 pp.

[52] Michael Gekhtman, Tomoki Nakanishi,
Asymptotic sign coherence conjecture,
Experimental Mathematics 31 (2022) 497--505; DOI:10.1080/10586458.2019.1650401.
arXiv:1904.00971, 13 pp.

[51] Michael Gekhtman, Tomoki Nakanishi, Dylan Rupel,
Hamiltonian and Lagrangian formalisms of mutations in cluster algebras and application to dilogarithm identities,
J. Integrable Syst. 2 (2017) 1--35 , (open access); DOI:10.1093/integr/xyx005.
arXiv:1611.02813, 31 pp.

[50] Tomoki Nakanishi,
Rogers dilogarithms of higher degree and generalized cluster algebras,
J. Math. Soc. Japan 70 (2018) 1269--1304; DOI:10.2969/jmsj/75767576.
arXiv:1605.0477, 32 pp.

[49] Tomoki Nakanishi, Dylan Rupel,
Companion cluster algebras to a generalized cluster algebra,
Travaux mathématiques 24 (2016) 129--149 , (open access).
arXiv:1504.06758, 14 pp.

[48] Tomoki Nakanishi,
Quantum generalized cluster algebras and quantum dilogarithms of higher degrees,
Theor. Math. Phys. 185 (2015) 1759--1768; DOI:10.1007/s11232-015-0377-9.
arXiv:1410.0584, 10 pp.

[47] Tomoki Nakanishi,
Structure of seeds in generalized cluster algebras,
Pacific J. Math. 277 (2015) 201--218; (open access) DOI:10.2140/pjm.2015.277.201.
arXiv:1409.5967, 15 pp.
Addendum to "Structure of seeds in generalized cluster algebras",
arXiv:2406.07582, 1 pp.

[46] Kohei Iwaki, Tomoki Nakanishi,
Exact WKB analysis and cluster algebras II: simple poles, orbifold points, and generalized cluster algebras,
Int. Math. Res. Not. 2016 (2016) 4375--4417 ; DOI:10.1093/imrn/rnv270.
arXiv:1409.4641, 34 pp.

[45] Kohei Iwaki, Tomoki Nakanishi,
Exact WKB analysis and cluster algebras,
J. Phys. A: Math. Theor. 47 (2014) 474009; DOI:10.1088/1751-8113/47/47/474009.
arXiv:1401.7094, 104 pp.

[44] Tomoki Nakanishi, Salvatore Stella,
Wonder of sine-Gordon \(Y\)-systems,
Trans. Amer. Math. Soc. 368 (2016) 6835--6886; DOI:10.1090/tran/6505.
arXiv:1212.6853, 53 pp.

[43] Tomoki Nakanishi, Salvatore Stella,
Diagrammatic description of \(c\)-vectors and \(d\)-vectors of cluster algebras of finite type,
Electron. J. Combin. 21 (2014) #P1.3, 107 pp. (open access)
arXiv:1210.6299, 108 pp.

[42] Tomoki Nakanishi,
Note on dilogarithm identities from nilpotent double affine Hecke algebras,
SIGMA 8 (2012) 104, 5 pp. (open access)
arXiv:1210.0226, 5 pp.

[41] Tomoki Nakanishi,
Tropicalization method in cluster algebras,
Contemp. Math. 580 (2012) 95--115.
arXiv:1110.5472, 21 pp.

[40] Rinat M. Kashaev, Tomoki Nakanishi,
Classical and quantum dilogarithm identities,
SIGMA 7 (2011) 102, 29 pp. (open access)
arXiv:1104.4630, 29 pp.

[39] Tomoki Nakanishi, Andrei Zelevinsky,
On tropical dualities in cluster algebras,
Contemp. Math. 565 (2012) 217--226.
arXiv:1101.3736, 10 pp.

[38] Rei Inoue, Tomoki Nakanishi,
Difference equations and cluster algebras I: Poisson bracket for integrable difference equations,
RIMS Kokyuroku Bessatsu B28 (2011) 63--88. (open access)
arXiv:1012.5574, 21 pp.

[37] Atsuo Kuniba, Tomoki Nakanishi, Junji Suzuki,
\(T\)-systems and \(Y\)-systems in integrable systems,
J. Phys. A: Math. Theor. 44 (2011) 103001 (146pp).
arXiv:1010.1344, 156 pp.

[36] Tomoki Nakanishi,
Periodicities in cluster algebras and dilogarithm identities,
(title chaged from the ealier version: Periodic cluster algebras and dilogarithm identities)
in Representations of algebras and related topics (A. Skowronski and K. Yamagata, eds.),
EMS Series of Congress Reports, European Mathematical Society, 2011, pp.407-444,
arXiv:1006.0632, 37 pp.

[35] Tomoki Nakanishi, Roberto Tateo,
Dilogarithm identities for sine-Gordon and reduced sine-Gordon \(Y\)-systems,
SIGMA 6 (2010) 085, 34 pp. (open access)
arXiv:1005.4199, 34 pp.

[34] Tomoki Nakanishi,
\(T\)-systems, \(Y\)-systems, and cluster algebras: Tamely laced case,
in New Trends in Quantum Integrable Systems (B. Feigin et al., eds.),
World Scientific, Singapore, 2011, pp. 325--355.
arXiv:1003.1180, 31 pp.

[33] Rei Inoue, Osamu Iyama, Bernhard Keller, Atsuo Kuniba, Tomoki Nakanishi,
Periodicities of \(T\) and \(Y\)-systems, dilogarithm identities, and cluster algebras II: Types \(C_r\), \(F_4\), and \(G_2\),
Publ. RIMS. 49 (2013) 43--85. (open access)
arXiv:1001.1881, 36 pp.

[32] Rei Inoue, Osamu Iyama, Bernhard Keller, Atsuo Kuniba, Tomoki Nakanishi,
Periodicities of \(T\) and \(Y\)-systems, dilogarithm identities, and cluster algebras I: Type \(B_r\),
Publ. RIMS. 49 (2013) 1--42. (open access)
arXiv:1001.1880, 35 pp.

[31] Tomoki Nakanishi,
Dilogarithm identities for conformal field theories and cluster algebras: simply laced case,
Nagoya Math. J. 202 (2011) 23--43. (open access)
arXiv:0909.5480, 16 pp.

[30] Atsuo Kuniba, Tomoki Nakanishi, Junji Suzuki,
\(T\)-systems and \(Y\)-systems for quantum affinizations of quantum Kac-Moody algebras,
SIGMA 5 (2009) 108, 23 pp. (open access)
arXiv:0909.4618, 23 pp.

[29] Rei Inoue, Osamu Iyama, Atsuo Kuniba, Tomoki Nakanishi, Junji Suzuki,
Periodicities of \(T\)-systems and \(Y\)-systems,
Nagoya Math. J. 197 (2010) 59--174. (open access)
arXiv:0812.0667, 83 pp.

[28] Wakako Nakai, Tomoki Nakanishi,
On Frenkel-Mukhin algorithm for \(q\)-character of quantum affine algebras,
Adv. Stud. Pure Math. 61 (2011) 327--347. (open access)
arXiv:0801.2239, 19 pp.

[27] Wakako Nakai, Tomoki Nakanishi,
Paths and tableaux descriptions of Jacobi-Trudi determinant associated with quantum affine algebra of type \(C_n\),
SIGMA 3 (2007) 078, 20 pp. (open access)
arXiv:math/0604158, 20 pp.

[26] Wakako Nakai, Tomoki Nakanishi,
Paths and tableaux descriptions of Jacobi-Trudi determinant associated with quantum affine algebra of type \(D_n\),
J. Alg. Combin. 26 (2007) 253-290.
arXiv:math/0603160, 38 pp.

[25] Wakako Nakai, Tomoki Nakanishi,
Paths, tableaux, and \(q\)-characters of quantum affine algebras: the \(C_n\) case,
J. Phys. A: Math. Gen. 39 (2006) 2083-2115.
arXiv:math/0502041, 38 pp.

[24] Atsuo Kuniba, Tomoki Nakanishi, Zengo Tsuboi,
The canonical solutions of the \(Q\)-systems and the Kirillov-Reshetikhin conjecture,
Commun. Math. Phys. 227 (2002) 155--190.
arXiv:math/0105145, 38 pp.

[23] Atsuo Kuniba, Tomoki Nakanishi, Zengo Tsuboi,
The Bethe equation at \(q=0\), the Mobius inversion formula, and weight multiplicities III: The \(X^{(r)}_n\) case,
Lett. Math. Phys. 59 (2002) 19--31.
arXiv:math/0105146, 11 pp.

[22] Atsuo Kuniba, Tomoki Nakanishi,
The Bethe equation at \(q=0\), the Mobius inversion formula, and weight multiplicities II: The \(X_n\) case,
J. Algebra 251 (2002) 577--618.
arXiv:math/0008047, 32 pp.

[21] Atsuo Kuniba, Tomoki Nakanishi,
The Bethe equation at \(q=0\), the Mobius inversion formula, and weight multiplicities I: The \(sl(2)\) case,
Progr. in Math. 191 (2000) 185--216.
arXiv:math/9909056, 35 pp.

[20] Anatol N. Kirillov, Atsuo Kuniba, Tomoki Nakanishi,
Skew Young diagram method in spectral decomposition of integrable lattice models II: Higher levels,
Nucl. Phys. B529 [PM] (1998) 611--638.
arXiv:q-alg/9711009, 27 pp.

[19] Anatol N. Kirillov, Atsuo Kuniba, Tomoki Nakanishi,
Skew Young diagram method in spectral decomposition of integrable lattice models,
Comm. Math. Phys. 185 (1997) 441--465.
arXiv:q-alg/9607027, 27 pp.

[18] Tomoyuki Arakawa, Tomoki Nakanishi, Kazuyuki Oshima, Akihiro Tsuchiya,
Spectral decomposition of path space in solvable lattice models,
Comm. Math. Phys. 181 (1996) 157--182.
arXiv:q-alg/9507025, 27 pp.

[17] Tomoki Nakanishi,
Fusion, mass, and representation theory of the Yangian algebra,
Nucl. Phys. B439 (1995) 441--459.
arXiv:hep-th/9405200, 21 pp.

[16] Atsuo Kuniba, Tomoki Nakanishi, Junji Suzuki,
Functional relations in solvable lattice models II: Applications,
Int. J. Mod. Phys. A9 (1994) 5267--5312.
arXiv:hep-th/9310060, 47 pp.

[15] Atsuo Kuniba, Tomoki Nakanishi, Junji Suzuki,
Functional relations in solvable lattice models I: Functional relations and representation theory,
Int. J. Mod. Phys. A9 (1994) 5215--5266.
arXiv:hep-th/9309137, 57 pp.

[14] Atsuo Kuniba, Tomoki Nakanishi, Junji Suzuki,
Characters in conformal field theories from thermodynamic Bethe ansatz,
Mod. Phys. Lett. A8 (1993) 1649--1659.
arXiv:hep-th/9301018 (TeX compling problem, not recommended). preprint pdf file (recommended), 12 pp.

[13] Atsuo Kuniba, Tomoki Nakanishi,
Rogers dilogarithm in integrable systems,
in Differential Geometric Methods in Theoretical Physics: Proceedings of the XXI International Conference (M.-L. Ge et al., eds.),
World Scientific, Singapore, 1993, pp.419--422.
arXiv:hep-th/9210025, 5 pp.

[12] Atsuo Kuniba, Tomoki Nakanishi,
Spectra in conformal field theories from the Rogers dilogarithm,
Mod. Phys. Lett. A7 (1992) 3487--3494.
arXiv:hep-th/9206034, 10 pp.

[11] Boris L. Feigin, Tomoki Nakanishi, Hirosi Ooguri,
The annihilating ideals of minimal models,
Int. J. Mod. Phys. A7, Suppl. 1A (1992) 217--238.
(available upon request)

[10] Atsuo Kuniba, Tomoki Nakanishi,
Fusion RSOS models and rational coset models,
in Quantum Groups (P. P. Kulish, ed.),
Lecture Notes in Math.1510 (1992) 303--311.
(available upon request)

[9] Tomoki Nakanishi, Akihiro Tsuchiya,
Level-rank duality in WZW models in conformal field theory,
Commun. Math. Phys. 144 (1992) 351--372. (open access)

[8] Rinat Kashaev, Vladimir V. Mangazeev, Tomoki Nakanishi,
Yang-Baxter equation for the \(sl(n)\) chiral Potts model,
Nucl. Phys. B362 (1991) 563--582.
(available upon request)

[7] Frederick M. Goodman, Tomoki Nakanishi,
Fusion algebras in integrable systems in two dimensions,
Phys. Lett. B262 (1991) 259-264.
(available upon request)

[6] Atsuo Kuniba, Tomoki Nakanishi, Junji Suzuki,
Ferro- and antiferro-magnetization in RSOS models,
Nucl. Phys. B356 (1991) 750--774.
(available upon request)

[5] Atsuo Kuniba, Tomoki Nakanishi,
Level-rank duality in fusion RSOS models,
in International Colloquium on Modern Quantum Field Theory (S. Das et al., eds.),
World Scientific, Singapore, 1991, pp.344--374, Errata p.567.
preprint pdf file.

[4] Tomoki Nakanishi,
Non-unitary minimal models and RSOS models,
Nucl. Phys. B334 (1990) 745--766.
(available upon request)

[3] Akishi Kato, Tomoki Nakanishi,
Differential equations in \(g \geq 2\) conformal field theory,
Mod. Phys. Lett. A4 (1989) 1773--1782.
(available upon request)

[2] Tomoki Nakanishi,
Radical root structure of conformal algebra,
Prog. Theor. Phys. 82 (1989) 207--214 . (open access)

[1] Tomoki Nakanishi,
Generalized supersymmetry on Riemann surfaces and the associated string models,
Mod. Phys. Lett. A3 (1988) 1507--1519.
(available upon request)