Publications

Monographs (peer-reviewed)

1. T. Kobayashi, T. Kubo, and M. Pevzner, Conformal symmetry breaking operators for differential forms on spheres. Lecture Notes in Math., vol. 2170, ix+192 pages, Springer-Nature, 2016.

English translation

1. Recent advances in branching problems of representations, Sugaku Expositions 37 (2024), 129-177.

Articles (peer-reviewed)

1. T. Kubo, Differential symmetry breaking operators from a line bundle to a vector bundle over real projective spaces, to appear in the proceedings of the Tunisian-Japanese conference: "Geometric and Harmonic Analysis on Homogeneous Spaces and Applications"  in honor of Professor Toshiyuki Kobayashi.

2. T. Kubo and B. Ørsted, Classification of K-type formulas for the Heisenberg ultrahyperbolic operator ◻s for SL˜(3,ℝ) and tridiagonal determinants for local Heun functions, M. Pevzner, H. Sekiguchi (eds.), Symmetry in Geometry and Analysis, Volume 2, Festschrift in Honor of Toshiyuki Kobayashi,  303-382, Progress in Math. 358, Birkhäuser Singapore, 2025. 

3. T. Kubo and B. Ørsted, On the intertwining differential operators from a line bundle to a vector bundle over the real projective space,  Indag. Math. 36 (2025), pp. 270-301 (the special issue dedicated to the memory of Gerrit van Dijk). 

4. H. He, T. Kubo, and R. Zierau, On the reducibility of scalar generalized Verma modules associated to maximal parabolic subalgebras. Kyoto J. Math. 59 (2019), pp. 787-813.

5. T. Kubo and B. Ørsted, On the space of K-finite solutions to intertwining differential operators. Represent. Theory 23 (2019), pp. 213-248.

6. T. Kobayashi, T. Kubo, and M. Pevzner, Conformal symmetry breaking operators for anti-de Sitter spaces. P. Kielanowski, A. Odzijewicz, E. Previato (eds.), Geometric Methods in Physics XXXV, 75-91, Trends Math. Birkhäuser, Cham, 2018.

7.  T. Kubo, On reducibility criterions for scalar generalized Verma modules associated to maximal parabolic subalgebras. V. Dobrev (ed.), Lie Theory and Its Applications in Physics, 465--473, Springer Proc. Math. & Stat. 191, Springer, Tokyo, 2016.

8. T. Kobayashi, T. Kubo, and M. Pevzner, Classification of differential symmetry breaking operators for differential forms. C.R. Acad. Sci. Paris, Ser. I 354 (2016), 671-676. (Announcement)

9. T. Kobayashi, T. Kubo, and M. Pevzner, Vector-valued covariant differential operators for the Mobius transformation. V. Dobrev (ed.), Lie Theory and Its Applications in Physics, 67-86, Springer Proc. Math. & Stat. 111, Springer, Tokyo, 2014.

10.  T. Kubo, Special values for conformally invariant systems associated to maximal parabolics of quasi-Heisenberg type. Trans. Amer. Math. Soc. 366 (2014), 4649-4696.

11. T. Kubo, The Dynkin index and conformally invariant systems associated to parabolic subalgebras of Heisenberg type. Osaka J. Math, 51 (2014), no. 2, 359-373.

12. T. Kubo, Systems of differential operators and generalized Verma modules. SIGMA Symmetry Integrability Geom. Methods Appl., 10 (2014), no. 008, 35 pages.

13. T. Kubo, On the homomorphisms between the generalized Verma modules arising from conformally invariant systems. J. Lie Theory, 23 (2013), no. 3, 847-883.

14. T. Kubo, Conformally invariant systems of differential operators associated to maximal parabolics of quasi-Heisenberg type. Proc. Japan Acad. Ser. A Math. Sci., 89 (2013), no. 3, 41-46. (Announcement)

15.  T. Kubo, A system of third-order differential operators conformally invariant under sl(3, C) and so(8, C). Pacific J. Math., 253 (2011), no. 2, 439-453.

Articles (Non-peer-reviewed)

1. T. Kubo and M. Pevzner, Symmetry Breaking, F-Method, and Beyond, Section VI of the chapter, The Mathematical Work of Toshiyuki Kobayashi, M. Pevzner, H. Sekiguchi (eds.), Symmetry in Geometry and Analysis, Volume 1, Festschrift in Honor of Toshiyuki Kobayashi,  55-68, Progress in Math. 357, Birkhäuser Singapore, 2025. 

2. T. Kubo, On the classification and construction of intertwining differential operators by the F-method (in Japanese). In H. Nakashima and A. Wachi, editors, Proceedings of Symposium on Representation Theory 2022, (2022), 25 pages.

3. T. Kubo, An algorithm on determining the reducibility points for generalized Verma modules of scalar type (Japanese). RIMS Workshop 2017: Representation Theory and Related Areas, RIMS Kôkyûroku, no. 2077 (2018), 106-116.

4.  T. Kobayashi, T. Kubo, and M. Pevzner, Conformal differential symmetry breaking operators for differential forms on spheres (Japanese). In H. Sekiguchi and K. Taniguchi, editors, Proceedings of Symposium on Representation Theory 2017, (2017), 132-143.

5. T. Kubo, Differential symmetry breaking operators of O(n,1) for differential forms (Japanese). In Abstract of the Functional Analysis Session (Special Session) at the MSJ 2017 Autumn Meeting, (2017) 45-54.

6. T. Kubo, The Dynkin index and parabolic subalgebra of Heisenberg type (Japanese). RIMS Workshop 2014: New Developments of Representation Theory and Harmonic Analysis, RIMS Kôkyûroku, no. 1925 (2014), 73-77.

7.   T. Kobayashi, T. Kubo, and M. Pevzner, Covariant differential operators and the Rankin--Cohen bracket (Japanese). In J. Matsuzawa and N. Shimeno, editors, Proceedings of Symposium on Representation Theory 2014, (2014), 75-86.

8. T. Kubo, On the F-method for constructing intertwining differential operators between homogeneous vector bundles. In M. Izumisawa and T. Kajiwara, editors, Real Analysis -- Functional Analysis Joint Symposium 2014, (2014), 85-95.

9. T. Kubo, On constructing explicit homomorphisms between generalized Verma modules. RIMS Workshop 2013: Development of Representation Theory and its Related Fields, RIMS Kôkyûroku, no. 1877 (2014), 142-151.

10. T. Kubo, On the homomorphisms between generalized Verma modules arising from conformally invariant systems. Representations of Lie Groups and Supergroups, Oberwolfach report (2013).

11. T. Kubo, On the homomorphisms between generalized Verma modules arising from conformally invariant systems. In M. Itoh and H. Ochiai, editors, Proceedings of Symposium on Representation Theory 2012, (2012), 143-154.

Ph.D. Thesis

• Conformally invariant systems of differential operators associated to two-step nilpotent maximal parabolics of non-Heisenberg type. ProQuest LLC, Ann Arbor, MI, 2012. Thesis (Ph.D.)--Oklahoma State University.

Preprints

• T. Kubo and B. Ørsted, On the intertwining differential operators between vector bundles over the real projective space of dimension two (submitted)

• T. Kubo and V. Pérez-Valdés, Truncated symbols of differential symmetry breaking operators