@inbook{704e149ba43c494991a45182253f8cc5,
title = "Classification of K-type Formulas for the Heisenberg Ultrahyperbolic Operator □s for SL(3,ℝ) and Tridiagonal Determinants for Local Heun Functions",
abstract = "The K-type formulas of the space of K-finite solutions to the Heisenberg ultrahyperbolic equation □sf=0 for the nonlinear group SL˜(3,ℝ) are classified. This completes a previous study of Kable for the linear group SL(m,ℝ) in the case of m=3, as well as generalizes our earlier results on a certain second-order differential operator. As a by-product we also show “functional equations” of certain sequences \{Pk(x;y)\}k=0∞ and \{Qk(x;y)\}k=0∞ of tridiagonal determinants, whose generating functions are given by local Heun functions.",
keywords = "05B20, 33C05, 33E30, Cayley continuant, Heisenberg ultrahyperbolic operator, Heun{\textquoteright}s differential equation, Hypergeometric differential equation, Intertwining differential operator, Krawtchouk polynomial, Primary 22E46; Secondary 17B10, Sylvester determinant, Tridiagonal determinant",
author = "Toshihisa Kubo and Bent {\O}rsted",
note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2025.",
year = "2025",
doi = "10.1007/978-981-97-7662-7\_8",
language = "English",
isbn = "978-981-97-7661-0",
volume = "2",
series = "Progress in Mathematics",
publisher = "Birkhauser",
pages = "303--382",
editor = "Michael Pevzner and Hideko Sekiguchi",
booktitle = "Symmetry in Geometry and Analysis",
}