### Abstract

In this paper we construct the fundamental solution to the Schödinger equation on a compact symmetric space with even root multiplicities using shift operators of Heckman and Opdam. Next, we prove that the support of the fundamental solution becomes a lower dimensional subset at a rational time whereas its support and its singular support coincide with the whole symmetric space at an irrational time. Moreover, we also show that generalized Gauss sums appear in the expression of the fundamental solution.

Original language | English |
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Pages (from-to) | 2739-2763 |

Number of pages | 25 |

Journal | Advances in Mathematics |

Volume | 226 |

Issue number | 3 |

DOIs | |

Publication status | Published - Feb 15 2011 |

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### Keywords

- Compact symmetric spaces
- Even multiplicity
- Fundamental solution
- Gauss sum
- Schödinger equation
- Shift operator
- Support

### ASJC Scopus subject areas

- Mathematics(all)