Matrix Valued Commuting Differential Operators with \(A_2\) Symmetry

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 207)


We study the algebra of invariant differential operators on a certain homogeneous vector bundle over a Riemannian symmetric space of type \(A_2\). We computed radial parts of its generators explicitly to obtain matrix-valued commuting differential operators with \(A_2\) symmetry. Moreover, we generalize the commuting differential operators with respect to a parameter and the potential function.


Matrix valued differential operators Matrix valued spherical functions Root system of type \(A_2\) 

2000 Mathematics Subject Classification

22E45 33C67 43A90 



The author would like to thank Professor Toshio Oshima, Professor Hiroyuki Ochiai, Professor Hiroshi Oda, and Professor Simon Ruijsenaars for helpful discussions and comments. The author would like to thank the referee for carefully reading the manuscript and for giving valuable comments.


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.School of Science & TechnologyKwansei Gakuin UniversitySandaJapan

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