Hideto Nakashima

Papers

1. An example of homogeneous cones whose basic relative invariant has maximal degree, to appear in the Proceedings of 7th Tunisian-Japanese Conference; arXiv:2405.09089.
2. Capelli-type identities and b-functions of prehomogeneous vector spaces associated with sub-Hankel determinants, to appear in Kyushu J. Math.
3. Decomposition of gamma matrices of local zeta functions associated with homogeneous cones, to appear in Tohoku Math. J. 76 (2024); arXiv:2112.15262.
4. Stieltjes transforms and $R$-transforms associated to two-parameter Lambert-Tsallis functions, Entropy 2023, 25(6), 858 (20 pages), joint work with P. Graczyk (Université d'Angers); Entropy.
5. Prehomogeneous vector spaces obtained from triangle arrangements, J. Algebra 633 (2023), 591--618, joint wirk with T. Kogiso (Josai University); J.Algebra.
6. Wigner and Wishart ensembles for sparse Vinberg models, Ann. Inst. Stats. Math. 74 (2022), 1--31, joint work with P. Graczyk (Université d'Angers); AISM.
7. Rings of invariant differential operators on homogeneous cones and their Capelli-type formulas, In: Baklouti A., Ishi H. (eds) Geometric and Harmonic Analysis on Homogeneous Spaces and Applications. TJC 2019. PROMS 366, Springer.
8. Functional equations of zeta functions associated with homogeneous cones, Tohoku Math. J. 72 (2020), 349--378; TMJ.
9. A shorter proof of a characterization of symmetric cones by the degrees of the basic relative invariants,
   Kyushu J. Math. 71 (2017), 251--255; KJM
10. Basic relative invariants of homogeneous cones and their Laplace transforms,
    J. Math. Soc. Japan 70 (2018), 1, 323--342; JMSJ
11. Characterization of symmetric cones by means of the basic relative invariants,
    Adv. Pure Appl. Math. 7 (2016), 2, 143--153; APAM
12. Basic relative invariants of homogeneous cones,
    Journal of Lie Theory 24 (2014), 1013--1032; JLT
13. Clans defined by representations of Euclidean Jordan algebras and the associated basic relative invariants,
    Kyushu J. Math. 67 (2013), 163--202, joint worh with T. Nomura; KJM

Others

1. Algebraic proof of explicit formulas of basic relative invariants of homogengeous cones, preprint. arXiv:2011.12588
2. Completion of local zeta functions associated with a certain class of homogeneous cones, preprint; arXiv:2011.11945.

Visit/Stay Abroad

1. Monastir, Tunisia 2023 November (7th TJC)
2. Marseille, France 2020 July (replaced online conference due to Covid-19, MMMS2)
3. New York, USA; 2020 May (cancelled due to Covid-19, RMTA-2020)
4. Djerba, Tunisia; 2019 December (TJC2019)
5. Université d'Angers (Professor Graczyk), France; 2019 December
6. Université d'Angers (Professor Graczyk), France; 2018 Dec. -- 2019 Mar.
7. Marseille, France; 2017 July (Luminy, MMMS)