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Research Output 1992 2019

  • 1586 Citations
  • 21 h-Index
  • 113 Article
  • 1 Comment/debate
  • 1 Review article
2019

DAHA and skein algebra of surfaces: double-torus knots

Hikami, K., Oct 1 2019, In : Letters in Mathematical Physics. 109, 10, p. 2305-2358 54 p.

Research output: Contribution to journalArticle

Affine Hecke Algebra
Torus knot
algebra
Algebra
polynomials
1 Citation (Scopus)
Open Access
Character Variety
Cluster Algebra
Cubic Surface
Poisson Algebra
Quantum Algebra
2017
1 Citation (Scopus)

Hecke-type formulas for families of unified Witten-Reshetikhin-Turaev invariants

Hikami, K. & Lovejoy, J., Jan 1 2017, In : Communications in Number Theory and Physics. 11, 2, p. 249-272 24 p.

Research output: Contribution to journalArticle

Torus knot
surgery
Surgery
Invariant
Colored Jones Polynomial
2015
9 Citations (Scopus)

Braids, complex volume and cluster algebras

Hikami, K. & Inoue, R., Oct 10 2015, In : Algebraic and Geometric Topology. 15, 4, p. 2175-2194 20 p., A008.

Research output: Contribution to journalArticle

Cluster Algebra
Braid
Octahedron
Knot
Mutation
12 Citations (Scopus)

Torus knots and quantum modular forms

Hikami, K. & Lovejoy, J., Dec 1 2015, In : Research in Mathematical Sciences. 2, 1, 2.

Research output: Contribution to journalArticle

Torus knot
Q-series
Modular Forms
Colored Jones Polynomial
Left handed
2014
9 Citations (Scopus)

Braiding operator via quantum cluster algebra

Hikami, K. & Inoue, R., Nov 28 2014, In : Journal of Physics A: Mathematical and Theoretical. 47, 47, 474006.

Research output: Contribution to journalArticle

Cluster Algebra
Quantum Algebra
Algebra
Mathematical operators
algebra
7 Citations (Scopus)

Cluster algebra and complex volume of once-punctured torus bundles and 2-bridge links

Hikami, K. & Inoue, R., Jan 1 2014, In : Journal of Knot Theory and its Ramifications. 23, 1, 1450006.

Research output: Contribution to journalArticle

Cluster Algebra
Bundle
Torus
Complement
Canonical Decomposition
2013
8 Citations (Scopus)

Enriques moonshine

Eguchi, T. & Hikami, K., Aug 9 2013, In : Journal of Physics A: Mathematical and Theoretical. 46, 31, 312001.

Research output: Contribution to journalArticle

Elliptic Genus
Symmetry Group
symmetry
2012
7 Citations (Scopus)

N=2 moonshine

Eguchi, T. & Hikami, K., Oct 22 2012, In : Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics. 717, 1-3, p. 266-273 8 p.

Research output: Contribution to journalArticle

algebra
6 Citations (Scopus)

Twisted Elliptic Genus for K3 and Borcherds Product

Eguchi, T. & Hikami, K., Nov 1 2012, In : Letters in Mathematical Physics. 102, 2, p. 203-222 20 p.

Research output: Contribution to journalArticle

Elliptic Genus
K3 Surfaces
Conjugacy class
Siegel Modular Forms
products
2011
62 Citations (Scopus)

Note on twisted elliptic genus of K3 surface

Eguchi, T. & Hikami, K., Jan 3 2011, In : Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics. 694, 4-5, p. 446-455 10 p.

Research output: Contribution to journalArticle

proposals
decomposition
expansion
symmetry
coefficients
9 Citations (Scopus)

On the modularity of the unified WRT invariants of certain Seifert manifolds

Bringmann, K., Hikami, K. & Lovejoy, J., Jan 1 2011, In : Advances in Applied Mathematics. 46, 1-4, p. 86-93 8 p.

Research output: Contribution to journalArticle

Seifert Manifold
Mock theta Functions
Modularity
Trefoil
Invariant
2010
6 Citations (Scopus)

N = 2 Superconformal algebra and the entropy of calabi-yau manifolds

Eguchi, T. & Hikami, K., Apr 7 2010, In : Letters in Mathematical Physics. 92, 3, p. 269-297 29 p.

Research output: Contribution to journalArticle

Calabi-Yau Manifolds
algebra
Calabi-Yau
Entropy
entropy
8 Citations (Scopus)

N = 4 superconformal algebra and the entropy of hyperKähler manifolds

Eguchi, T. & Hikami, K., Jul 30 2010, In : Journal of High Energy Physics. 2010, 2, 019.

Research output: Contribution to journalArticle

algebra
entropy
decomposition
expansion
products
13 Citations (Scopus)
Vertex Model
Spin Chains
One-dimensional Model
Partition Function
Schur Polynomials
2009
20 Citations (Scopus)

Superconformal algebras and mock theta functions

Eguchi, T. & Hikami, K., Nov 23 2009, In : Journal of Physics A: Mathematical and Theoretical. 42, 30, 304010.

Research output: Contribution to journalArticle

Mock theta Functions
Elliptic Genus
Algebra
algebra
Jacobi Forms
24 Citations (Scopus)

Superconformal algebras and mock theta functions 2: Rademacher expansion for K3 surface

Eguchi, T. & Hikami, K., Sep 2009, In : Communications in Number Theory and Physics. 3, 3, p. 531-554 24 p.

Research output: Contribution to journalArticle

Elliptic Genus
Mock theta Functions
K3 Surfaces
algebra
Algebra
2008
4 Citations (Scopus)

Colored Jones polynomials with polynomial growth

Hikami, K. & Murakami, H., Nov 1 2008, In : Communications in Contemporary Mathematics. 10, SUPPL. 1, p. 815-834 20 p.

Research output: Contribution to journalArticle

Colored Jones Polynomial
Hyperbolic Knot
Alexander Polynomial
Polynomial Growth
Complex number

Duality of linking pairing in arnold's singularities

Hikami, K., Jul 1 2008, In : Proceedings of the Japan Academy Series A: Mathematical Sciences. 84, 7, p. 81-86 6 p.

Research output: Contribution to journalArticle

Pairing
Linking
Duality
Seifert Manifold
Singularity
21 Citations (Scopus)
registers
elementary excitations
entropy
matrices
2007
5 Citations (Scopus)

Asymptotics of the colored Jones polynomial and the A-polynomial

Hikami, K., Jul 2 2007, In : Nuclear Physics B. 773, 3, p. 184-202 19 p.

Research output: Contribution to journalArticle

polynomials
18 Citations (Scopus)

Boson-fermion duality in SU (m | n) supersymmetric Haldane-Shastry spin chain

Basu-Mallick, B., Bondyopadhaya, N., Hikami, K. & Sen, D., Oct 22 2007, In : Nuclear Physics B. 782, 3, p. 276-295 20 p.

Research output: Contribution to journalArticle

bosons
fermions
symmetry
partitions
polynomials
46 Citations (Scopus)
Neumann function
Classical Limit
A-polynomial
Potential Function
Partition Function
8 Citations (Scopus)
Mock theta Functions
Higher Order
Invariant
Ramanujan
Colored Jones Polynomial
2006

Hypergeometric generating function of l-function, slater’s identities, and quantum invariant

Hikami, K. & Kirillov, A. N., Jan 1 2006, In : St. Petersburg Mathematical Journal. 17, 1, p. 143-156 14 p.

Research output: Contribution to journalArticle

Quantum Invariants
Hypergeometric Functions
Generating Function
Torus knot
Q-series
12 Citations (Scopus)

On the quantum invariants for the spherical Seifert manifolds

Hikami, K., Dec 1 2006, In : Communications in Mathematical Physics. 268, 2, p. 285-319 35 p.

Research output: Contribution to journalArticle

Seifert Manifold
Quantum Invariants
Modular Forms
Invariant
Invariant Polynomials
13 Citations (Scopus)

Q-Series and L-functions related to half-derivatives of the Andrews-Gordon identity

Hikami, K., Apr 1 2006, In : Ramanujan Journal. 11, 2, p. 175-197 23 p.

Research output: Contribution to journalArticle

Q-series
L-function
Generating Function
Quantum Invariants
Torus knot
6 Citations (Scopus)

Quantum invariants, modular forms, and lattice points II

Hikami, K., Nov 8 2006, In : Journal of Mathematical Physics. 47, 10, 102301.

Research output: Contribution to journalArticle

Quantum Invariants
Modular Lattice
Lattice Points
Modular Forms
Invariant
17 Citations (Scopus)

Transformation formula of the "second" order mock theta function

Hikami, K., Jan 1 2006, In : Letters in Mathematical Physics. 75, 1, p. 93-98 6 p.

Research output: Contribution to journalArticle

Seifert Manifold
Mock theta Functions
Quantum Invariants
Transformation Formula
2005
14 Citations (Scopus)

Integrable spin-boson interaction in the Tavis-Cummings model from a generic boundary twist

Amico, L. & Hikami, K., Feb 1 2005, In : European Physical Journal B. 43, 3, p. 387-391 5 p.

Research output: Contribution to journalArticle

Bosons
bosons
Boundary conditions
interactions
boundary conditions
26 Citations (Scopus)

Mock (false) theta functions as quantum invariants

Hikami, K., Dec 1 2005, In : Regular and Chaotic Dynamics. 10, 4, p. 509-530 22 p.

Research output: Contribution to journalReview article

Seifert Manifold
Mock theta Functions
Quantum Invariants
Theta Functions
Ramanujan
17 Citations (Scopus)

On the quantum invariant for the brieskorn homology spheres

Hikami, K., Jul 1 2005, In : International Journal of Mathematics. 16, 6, p. 661-685 25 p.

Research output: Contribution to journalArticle

Quantum Invariants
Homology Spheres
Invariant
Modular Forms
Casson Invariant
8 Citations (Scopus)

Quantum invariant, modular form, and lattice points

Hikami, K., Jan 18 2005, In : International Mathematics Research Notices. 3, p. 121-154 34 p.

Research output: Contribution to journalArticle

Quantum Invariants
Modular Lattice
Lattice Points
Modular Forms
2004
28 Citations (Scopus)

Difference equation of the colored Jones polynomial for torus knot

Hikami, K., Nov 1 2004, In : International Journal of Mathematics. 15, 9, p. 959-965 7 p.

Research output: Contribution to journalArticle

Colored Jones Polynomial
Torus knot
Difference equation
Second-order Difference Equations
A-polynomial
21 Citations (Scopus)

Quantum Invariant for Torus Link and Modular Forms

Hikami, K., Apr 1 2004, In : Communications in Mathematical Physics. 246, 2, p. 403-426 24 p.

Research output: Contribution to journalArticle

Quantum Invariants
Modular Forms
unity
Torus
expansion
2003
10 Citations (Scopus)

Topics in quantum integrable systems

Hikami, K. & Wadati, M., Aug 1 2003, In : Journal of Mathematical Physics. 44, 8, p. 3569-3594 26 p.

Research output: Contribution to journalArticle

Quantum Integrable Systems
polynomials
Dunkl Operators
Macdonald Polynomials
Yang-Baxter Equation
20 Citations (Scopus)

Torus knot and minimal model

Hikami, K. & Kirillov, A. N., Nov 27 2003, In : Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics. 575, 3-4, p. 343-348 6 p.

Research output: Contribution to journalArticle

integers
unity
polynomials
5 Citations (Scopus)

Vicious walkers and hook Young tableaux

Hikami, K. & Imamura, T., Mar 28 2003, In : Journal of Physics A: Mathematical and General. 36, 12 SPEC. ISS., p. 3033-3048 16 p.

Research output: Contribution to journalArticle

Tracy-Widom Distribution
Saddle Point Method
Young Tableaux
Young Diagram
hooks
17 Citations (Scopus)

Volume conjecture and asymptotic expansion of q-series

Hikami, K., Jan 1 2003, In : Experimental Mathematics. 12, 3, p. 319-337 19 p.

Research output: Contribution to journalArticle

Q-series
Asymptotic Expansion
Knot
Invariant
Borromean rings
2002
4 Citations (Scopus)

Hyperbolic structure arising from a knot invariant II: Completeness

Hikami, K., Jun 20 2002, In : International Journal of Modern Physics B. 16, 14-15, p. 1963-1970 8 p.

Research output: Contribution to journalArticle

completeness
saddle points
geometry
19 Citations (Scopus)

Quasi-classical descendants of disordered vertex models with boundaries

Di Lorenzo, A., Amico, L., Hikami, K., Osterloh, A. & Giaquinta, G., Nov 18 2002, In : Nuclear Physics B. 644, 3, p. 409-432 24 p.

Research output: Contribution to journalArticle

apexes
fermions
spin-spin coupling
boundary conditions
operators
2001
9 Citations (Scopus)

Hyperbolicity of partition function and quantum gravity

Hikami, K., Nov 26 2001, In : Nuclear Physics B. 616, 3, p. 537-548 12 p.

Research output: Contribution to journalArticle

partitions
gravitation
tetrahedrons
strings
geometry
28 Citations (Scopus)

Hyperbolic structure arising from a knot invariant

Hikami, K., Jul 30 2001, In : International Journal of Modern Physics A. 16, 19, p. 3309-3333 25 p.

Research output: Contribution to journalArticle

saddle points
polyhedrons
analogs
3 Citations (Scopus)

Mesoscopic Fluctuations in Superconducting Wires

Imamura, T. & Hikami, K., Nov 1 2001, In : journal of the physical society of japan. 70, 11, p. 3312-3321 10 p.

Research output: Contribution to journalArticle

shot noise
quantum wires
transport properties
wire
moments

Symmetry of integrable cellular automaton

Hikami, K. & Inoue, R., Mar 23 2001, In : Journal of Physics A: Mathematical and General. 34, 11, p. 2467-2476 10 p.

Research output: Contribution to journalArticle

cellular automata
Cellular automata
Difference equations
Cellular Automata
boxes
74 Citations (Scopus)

The A(1)M automata related to crystals of symmetric tensors

Hatayama, G., Hikami, K., Inoue, R., Kuniba, A., Takagi, T. & Tokihiro, T., Jan 1 2001, In : Journal of Mathematical Physics. 42, 1, p. 274-308 35 p.

Research output: Contribution to journalArticle

Soliton Solution
Automata
Solitons
Crystal
Tensor
10 Citations (Scopus)

The Baxter equation for quantum discrete Boussinesq equation

Hikami, K., Jun 25 2001, In : Nuclear Physics B. 604, 3, p. 580-602 23 p.

Research output: Contribution to journalArticle

operators
difference equations
2000
6 Citations (Scopus)

Supersymmetric extension of the integrable box-ball system

Hikami, K. & Inoue, R., Jun 9 2000, In : Journal of Physics A: Mathematical and General. 33, 22, p. 4081-4094 14 p.

Research output: Contribution to journalArticle

Crystal Bases
Time Operator
Evolution Operator
Lie Superalgebra
Soliton Solution
26 Citations (Scopus)

Supersymmetric Polychronakos spin chain: Motif, distribution function, and character

Hikami, K. & Basu-Mallick, B., Feb 7 2000, In : Nuclear Physics B. 566, 3, p. 511-528 18 p.

Research output: Contribution to journalArticle

distribution functions
elementary excitations
partitions
polynomials
fine structure
6 Citations (Scopus)

The lattice Toda field theory for simple Lie algebras: Hamiltonian structure and τ -function

Inoue, R. & Hikami, K., Aug 21 2000, In : Nuclear Physics B. 581, 3, p. 761-775 15 p.

Research output: Contribution to journalArticle

algebra