Oscillator representations and systems of ordinary differential equations

Alberto Parmeggiani, Masato Wakayama

Research output: Contribution to journalArticlepeer-review

41 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)26-30
Number of pages5
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number1
Publication statusPublished - Jan 2 2001

All Science Journal Classification (ASJC) codes

  • General


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