I have been working on mathematical aspects of 2D conformal field theories and related areas.
The research topics from new to old are roughly:
- Universal formulas of minimal nilpotent orbits.
- Finiteness properties of vertex operator algebras.
- 3-transposition automorphisms of vertex operator algebras
- Vertex operator algebras with large symmetries.
- Automophism groups of vertex operator algebras.
- Representation theory of quantum affine algebras.
- Knizhnik-Zamolodchikov equation and its variants.
Refereed Research Papers
A. Matsuo and A.P. Veselov: Universal formula for the Hilbert series of minimal nilpotent orbits.
Proceedings of the American Mathematical Society., 145, No.12, (2017), 5123--5130.
H. Maruoka, A. Matsuo and H. Shimakura: Classification of vertex operator algebras of class S4 with minimal conformal weight one.
Journal of Mathematical Society of Japan, 68, (2016), 1369--1388.
A Matsuo, K. Nagatomo and A. Tsuchiya: Quasi-finite algebras graded by Hamiltonian and vertex operator algebras.
Moonshine - The First Quarter Century and Beyond,
Proceedings of a Workshop on the Moonshine Conjectures and Vertex Algebras, London Mathematical Society Lecture Note Series No.\ 372, Cambridge University Press, 2010.
A. Matsuo: 3-transposition groups of symplectic type and vertex operator algebras.
Journal of Mathematical Society of Japan 57 (2005), no. 3, 639--649.
A Matsuo: Norton's trace formulae for the Griess algebra of a vertex operator algebra with larger symmetry.
Commun. Math. Phys. 224 (2001), 565--591.
A Matsuo and M Matsuo: The automorphism group of the Hamming code vertex operator
J. Algebra, 228 (2000), 204--226.
A Matsuo and K Nagatomo: A note on free bosonic vertex algebra and its conformal vectors.
J. Algebra 212 (1999), 395--418.
A Matsuo: A q-deformation of Wakimoto modules, primary fields, and screening operators.
Commun. Math. Phys. 160 (1994), 33--48.
A Matsuo: Quantum algebra structure of certain Jackson integrals.
Commun. Math. Phys., 157 (1993), 479--498.
A Matsuo: Free field representation of the quantum affine algebra Uq(sl^2).
Phys. Lett. B308 (1993), 260-265.
A Matsuo: Jackson integrals of Jordan-Pochhammer type and Quantum Knizhnik-Zamolodchikov equations.
Commun. Math. Phys., 151 (1993), 263--273.
A Matsuo: Integrable connections related to zonal spherical functions,
Invent. Math., 110 (1992), 95--121.
A Matsuo: An Application of Aomoto-Gelfand Hypergeometric Functions to SU(n) Knizhnik-Zamolodchikov Equation.
Commun. Math. Phys. 134 (1990), 65--77
- E Date, M Jimbo, A Matsuo and T Miwa: Hypergeometric type integrals and the sl(2,C) Knizhnik-Zamolodchikov equations.
Int. J. Mod. Phys. B4 (1990), 1049
A Matsuo and K Nagatomo: Axioms for a vertex algebra and the locality of quantum fields.
MSJ Memoirs 4, Math. Soc. Japan, 1999.
Summary of the theory of primitive forms.
Topological field theory, primitive forms, and related topics,
Japanese Papers and Books
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