## Abstract

We describe realizations of the color analogue

of the Heisenberg Lie algebra by power series in non-commuting indeterminates satisfying Heisenberg's canonical commutation relations of quantum mechanics. The obtained formulas are used to construct new operator

representations of the color analogue of the Heisenberg Lie algebra. These representations are shown to be closely connected with some combinatorial identities and functional difference-differential interpolation formulae involving Euler, Bernoulli and Stirling numbers.

of the Heisenberg Lie algebra by power series in non-commuting indeterminates satisfying Heisenberg's canonical commutation relations of quantum mechanics. The obtained formulas are used to construct new operator

representations of the color analogue of the Heisenberg Lie algebra. These representations are shown to be closely connected with some combinatorial identities and functional difference-differential interpolation formulae involving Euler, Bernoulli and Stirling numbers.

Original language | English |
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Number of pages | 46 |

Journal | Preprints in Mathematical Sciences |

Volume | 2003 |

Issue number | 4 |

Publication status | Unpublished - 2003 |

## Subject classification (UKÄ)

- Mathematics

## Keywords

- Heisenberg Lie algebra
- combinatorial identities
- representations
- functional difference-differential interpolation
- Bernoulli and Stirling numbers
- Euler