K. Hikami, "Askey-Wilson polynomials and genus-two skein module", [arXiv:25**.]
K. Hikami, "A Note on Double Affine Hecke Algebra for Skein Algebra on Twice-Punctured Torus", J. Geom. Phys. 209, 105408 (2025) [arXiv:2408:17021]
K. Hikami, "Generalized Double Affine Hecke Algebra for Double Torus", Lett. Math. Phys. 114, #102, 16 pages [arXiv:2402.09106]
K. Hikami and S. Sugimoto, "Torus links T(2s,2t) and (s,t)-log VOA", preprint [arXiv:2306.03338]
A. Beliakova and K. Hikami, "Non-semisimple invariants and Habiro series", in Topology and Geometry -- A Collection of Essays Dedicated to Vladimir G. Turaev, edited by Athanase Papadopoulos, pp. 161--174 (2021) [arXiv:2009.13285]
K. Hikami, "DAHA and skein algebra on surface: double-torus knots", Lett. Math. Phys. 109, 2305--2358 (2019) [arXiv:1901.02743]
K. Hikami, "Note on Character Varieties and Cluster Algebras", SIGMA 15, 003 (2019), 32 pages [arXiv:1711.03379]
K. Hikami and J. Lovejoy, "Hecke-type Formulas for Families of Unified Witten-Reshetikhin-Turaev Invariants", Commun. Number Theory and Physics 11, 249--272 (2017)
K. Hikami and J. Lovejoy, "Torus Knots and Quantum Modular Forms", Research in the Mathematical Sciences, 2:2 (2015), 15 pages [arXiv:1409.6243].
K. Hikami and R. Inoue, "Braiding Operator via Quantum Cluster Algebra", J. Phys. A: Math. Theor. 47, 474006 (2014), 21 pages [arXiv:1404.2009]
K. Hikami and R. Inoue, "Braids, Complex Volume, and Cluster Algebra", Algebraic & Geometric Topology 15, 2175--2194 (2015) [arXiv:1304.4776]
T. Eguchi and K. Hikami, "Enriques Moonshine", J. Phys. A: Math. Theor. 46, 312001 (2013), 11 pages [arXiv:1301.5043]
K. Hikami and R. Inoue, "Cluster Algebra and Complex Volume of Once-Punctured Torus Bundles and Two-Bridge Links", J. Knot Theory Ramifications 23, 1450006 (33 pages) (2014) [arXiv:1212.6042]
T. Eguchi and K. Hikami, "N=2 Moonshine", Phys. Lett. B 717, 266--273 (2012) [arXiv:1209.0610]
T. Eguchi and K. Hikami, "Twisted Elliptic Genus for K3 and Borcherds Product", Lett. Math. Phys. 102, 203--222 (2012) [arXiv:1112.5928]
K. Hikami and H. Murakami, "Representations and the Colored Jones Polynomial of a Torus Knot", in Chern-Simons Gauge Theory: 20 Years After, AMS/IP Studies in Advanced Mathematics 50, 153--171, 2011, AMS [arXiv:1001.2680]
K. Hikami, "Decomposition of Witten-Reshetikhin-Turaev Invariant: linking pairing and modular forms", in Chern-Simons Gauge Theory: 20 Years After, AMS/IP Studies in Advanced Mathematics 50, 131--151, 2011, AMS [PDF]
T. Eguchi and K. Hikami, "Note on Twisted Elliptic Genus of K3 Surface", Phys. Lett. B 694, 446--455 (2011) [arXiv:1008.4924]
K. Bringmann, K. Hikami, and J. Lovejoy, "On the Modularity of the Unified WRT Invariants of Certain Seifert Manifolds", Adv. Appl. Math. 46, 86--93 (2011) [PDF]
B. Basu-Mallick, N. Bondyopadhaya, and K. Hikami, "One-Dimensional Vertex Models Associated with a Class of Yangian Invariant Haldane-Shastry Like Spin Chains", SIGMA 6, 91 (2010), 13 pages [arXiv:1008.5285]
T. Eguchi and K. Hikami, "N=2 Superconformal Algebra and the Entropy of Calabi-Yau Manifolds", Lett. Math. Phys. 92, 269--297 (2010) [arXiv:1003.1555] [PDF]
T. Eguchi and K. Hikami, "N=4 Superconformal Algebra and the Entropy of HyperKahler Manifolds", JHEP 2010:02, 019 (2010), 28 pages. [arXiv:0909.0410]
T. Eguchi and K. Hikami, "Superconformal Algebras and Mock Theta Functions 2. Rademacher Expansion for K3 Surface", Commun. Number Theory Physics 3, 531--554 (2009) [arXiv:0904.0911] [PDF]
T. Eguchi and K. Hikami, "Superconformal Algebras and Mock Theta Functions", J. Phys. A: Math. Theor. 42, 304010 (2009), 23 pages. [arXiv:0812.1151]
K. Hikami and H. Murakami, "Colored Jones Polynomials with Polynomial Growth" Commun. Contemp. Math. 10 Suppl. 1, 815--834 (2008) [arXiv:0711.2836]
K. Hikami, "Skein Theory and Topological Quantum Registers: braiding matrices and topological entanglement entropy", Ann. Phys. 323, 1729--1769 (2008) [PDF] [arXiv:0709.2409]
B. Basu-Mallick, N. Bondyopadhaya, K. Hikami, and D. Sen, "Boson-Fermion Duality in SU(m|n) Supersymmetric Haldane-Shastry Spin Chain", Nucl. Phys. B 782, 276--295 (2007) [hep-th/0703240]
K. Hikami, "Duality of Linking Pairing in Arnold's Singularities", Proc. Japan Acad. Ser. A 87, 81--86 (2008)
K. Hikami, "Hecke Type Formula for Unified Witten-Reshetikhin-Turaev Invariant as Higher OrderMock Theta Functions", IMRN 2007, rnm022 (2007), 32 pages
K. Hikami, "Recent Topics on Relationship Between Quantum Invariants and Modular Forms", invited talk at Mathematical Society of Japan, September 2006. [PDF]
K. Hikami, "Generalized Volume Conjecture and the A-polynomials: the Neumann-Zagier potential Function as a classical limit of partition function", J. Geom. Phys. 57, 1895--1940 (2007) [arXiv:math/0604094] [PDF]
K. Hikami, "Quantum Invariants, Modular Forms, and Lattice Points II", J. Math. Phys. 47, 102301 (2006), 32 pages [math.QA/0604091]
K. Hikami, "Transformation Formula for the `2nd' Order Mock Theta Functions", Lett. Math. Phys. 75, 93--98 (2006) [math-ph/0604007]
K. Hikami, "Mock (false) Theta Functions as Quantum Invariants", Regular and Chaotic Dynamics 10, 509--530 (2005) [math-ph/0506073]
K. Hikami, "On the Quantum Invariant for the Spherical Seifert Manifolds" Commun. Math. Phy. 268, 285--319 (2006) [math-ph/0504082]
K. Hikami, "Quantum Invariants for Links and 3-Manifolds", Rikkyo University Kokyuroku (2005) [PDF]
K. Hikami, "Asymptotic Behavior of the WRT Invariant and Modular Form", talk at `Intelligence of Low-Dimensional Topology' (ILDT 2004), 2004 [PDF]
K. Hikami, "Quantum Invariant, Modular Form, and Lattice Points", IMRN 2005:3, 121--154 (2005) [math-ph/0409016]
K. Hikami, "Quantum Invariant for Torus Knot and Modular Form", talk at @3rd spring conference on modular form and related topics', Hamana-ko, 2004 [PDF]
K. Hikami, "Asymptotics of the Colored Jones Polynomial and the A-Polynomial", Nucl. Phys. B 773, 184--202 (2007) [math-ph/0407043]
K. Hikami and A. N. Kirillov, "Hypergeometric Generating Function for L-Functions, Slater's Identities, and Quantum Knot Invariants", St. Petersburg Math. J. 17, 143--156 (2006) [math-ph/0406042]
K. Hikami, "On the Quantum Invariant for the Brieskorn Homology Spheres", Int. J. Math. 16, 661--685 (2005) [math-ph/0405028]
K. Hikami, "Difference Equation of the Colored Jones Polynomial for Torus Knot", Int. J. Math. 15, 959--965 (2004) [math.GT/0403224]
L. Amico and K. Hikami, "Integrable Spin-Boson Interaction in the Tavis-Cummings Model From a Generic Boundary Twist", Euro. Phys. J. B 43, 387--391 (2005) [cond-mat/0309680]
K. Hikami and A. N. Kirillov, "Torus Knot and Minimal Model", Phys. Lett. B 575, 343--348 (2003) [hep-th/0308152]
K. Hikami, "Quantum Invariant for Torus Link and Modular Forms", Commun. Math. Phys. 246, 403--426 (2004) [math-ph/0305039]
K. Hikami, "q-Series and L-functions Related to Half-Derivatives of the Andrews--Gordon Identity", Ramanujan J. 11, 175--197 (2006) [math/0303250]
K. Hikami and T. Imamura, "Vicious Walkers and Hook Young Tableaux", J. Phys. A: Gen. Math. 36, 3033--3048 (2003) [cond-mat/0209512]
K. Hikami, "Volume Conjecture and Asymptotic Expansion of q-series", Exp. Math. 12, 319--337 (2003) [pdf]
K. Hikami, "Quantum Discrete Soliton Equations", in Kowalevsky Property, edited by V. Kuznetsov, CRM Proceedings and Lecture Notes 32, 93--120, AMS (2002)
K. Hikami, "Logarithmic Correction of Kashaev's Invariant", RIMS Kokyuroku 1279, 40--66 (2002)
A. D. Lorenzo, L. Amico, K. Hikami, A. Osterloh, and G. Giaquinta, "Quasi-classical descendants of disordered vertex models with boundaries", Nucl. Phys. B644, 409--432 (2002)
K. Hikami, "Hyperbolicity of Partition Function and Quantum Gravity", Nucl. Phys. B616, 537--548 (2001) [hep-th/0108009]
T. Imamura and K. Hikami, "Mesoscopic Fluctuations in Superconducting Wires", J. Phys. Soc. Jpn. 70, 3312--3321 (2001)
K. Hikami, "The Baxter Equation for Quantum Discrete Boussinesq Equation", Nucl. Phys. B604, 580--602 (2001) [nlin/0102021]
K. Hikami and R. Inoue, "Symmetry of Cellular Automaton", J. Phys. A: Math. Gen. 34, 2467--2476 (2001)
K. Hikami, "Hyperbolic Structure Arising from a Knot Invariant", Int. J. Mod. Phys. A 16, 3309--3333 (2001) [math-ph/0105039]
K. Hikami and R. Inoue, "Supersymmetric Extension of the Integrable Box-Ball System", J. Phys. A: Math. Gen. 33, 4081--4094 (2000)
B. Basu-Mallick and K. Hikami, "Supersymmetric Polychronakos spin chain: motifs, distribution functions, and characters", Nucl. Phys. B 566, 511--528 (2000)
K. Hikami, R. Inoue, and Y. Komori, "Crystallization of the Bogoyavlensky lattice", J. Phys. Soc. Jpn. 68, 2234--2240 (1999)
K. Hikami, "The ZN symmetric quantum lattice field theory: the quantum group symmetry, the Yang-Baxter equation, and the integrals of motion", J. Phys. Soc. Jpn. 68, 55--60 (1999)
K. Hikami, "Quantum group symmetry and integrals of motion in the Z3 symmetric lattice field theory", Phys. Lett. B 443, 202--207 (1998)
Y. Komori and K. Hikami, "Affine R-matrix and the generalized elliptic Ruijsenaars models", Lett. Math. Phys. 43, 335--346 (1998)
Y. Komori and K. Hikami, "Conserved operators of the generalized elliptic Ruijsenaars models", J. Math. Phys. 39, 6175--6190 (1998)
K. Hikami and Y. Komori, "Diagonalization of the elliptic Ruijsenaars model: correspondence with the Belavin model", Eur. Phys. J. B 5, 583--588 (1998)
K. Hikami and Y. Komori, "Boundary Boltzmann weight for the eight-vertex SOS model: vertex-IRF correspondence", J. Phys. Soc. Jpn. 67, 78--82 (1998)
K. Hikami, "Statistical mechanical interpretation of the inverse scattering method: level dynamics for the exclusion statistics", Phys. Rev. Lett. 80, 4374--4377 (1998)
K. Hikami, "Notes on the structure of the delta-function interacting gas: intertwining operator in the degenerate affine Hecke algebra", J. Phys. A: Math. Gen. 31, L85--L91 (1998)
K. Hikami, "On the fundamental L-operator for the quantum lattice W algebra", Chaos, Solitons & Fractals 9, 853--867 (1998)
Y. Komori and K. Hikami, "Quantum integrability of the generalized Ruijsenaars model", J. Phys. A: Math. Gen. 30, 4341--4364 (1997)
Y. Komori and K. Hikami, "Integrable three-body problems with two- and three-body interactions", J. Phys. A: Math. Gen. 30, 1913--1923 (1997)
K. Hikami, K. Sogo, and R. Inoue, "Hidden symmetry of the Bogoyavlensky lattice: the lattice W algebras and the vertex operator", J. Phys. Soc. Jpn. 66, 3756--3763 (1997)
K. Hikami and S. Murakami, "Integrability of a Hubbard-like model: lattice analogue of the delta-function interacting gas", Phys. Lett. A 221, 109--114 (1996)
K. Hikami, "Representation of motifs: new aspect of the Rogers-Szego polynomial", J. Phys. Soc. Jpn. 64, 1047--1050 (1995)