### Abstract

Using representation-theoretic methods, we determine the spectrum of the 2 × 2 system Q(x, D_{x}) = A(-∂_{x}/^{2}/2 + x^{2}/2) + B(x∂_{x} + 1/2), x ∈ R, with A,B ∈ Mat_{2}(R) constant matrices such that A = ^{t}A > 0 (or < 0), B = -^{t}B ≠ 0, and the Hermitian matrix A + iB positive (or negative) definite. We also give results that generalize (in a possible direction) the main construction.

Original language | English |
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Pages (from-to) | 26-30 |

Number of pages | 5 |

Journal | Proceedings of the National Academy of Sciences of the United States of America |

Volume | 98 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 2 2001 |

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### All Science Journal Classification (ASJC) codes

- General

### Cite this

**Oscillator representations and systems of ordinary differential equations.** / Parmeggiani, Alberto; Wakayama, Masato.

Research output: Contribution to journal › Article

*Proceedings of the National Academy of Sciences of the United States of America*, vol. 98, no. 1, pp. 26-30. https://doi.org/10.1073/pnas.98.1.26

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TY - JOUR

T1 - Oscillator representations and systems of ordinary differential equations

AU - Parmeggiani, Alberto

AU - Wakayama, Masato

PY - 2001/1/2

Y1 - 2001/1/2

N2 - Using representation-theoretic methods, we determine the spectrum of the 2 × 2 system Q(x, Dx) = A(-∂x/2/2 + x2/2) + B(x∂x + 1/2), x ∈ R, with A,B ∈ Mat2(R) constant matrices such that A = tA > 0 (or < 0), B = -tB ≠ 0, and the Hermitian matrix A + iB positive (or negative) definite. We also give results that generalize (in a possible direction) the main construction.

AB - Using representation-theoretic methods, we determine the spectrum of the 2 × 2 system Q(x, Dx) = A(-∂x/2/2 + x2/2) + B(x∂x + 1/2), x ∈ R, with A,B ∈ Mat2(R) constant matrices such that A = tA > 0 (or < 0), B = -tB ≠ 0, and the Hermitian matrix A + iB positive (or negative) definite. We also give results that generalize (in a possible direction) the main construction.

UR - http://www.scopus.com/inward/record.url?scp=0035793063&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035793063&partnerID=8YFLogxK

U2 - 10.1073/pnas.98.1.26

DO - 10.1073/pnas.98.1.26

M3 - Article

C2 - 11134511

AN - SCOPUS:0035793063

VL - 98

SP - 26

EP - 30

JO - Proceedings of the National Academy of Sciences of the United States of America

JF - Proceedings of the National Academy of Sciences of the United States of America

SN - 0027-8424

IS - 1

ER -