A nonstandard way of representing canonical anticommutation relations is presented. It is connected with a generalization of the Heisenberg group to the case of graded phase space. We show how Grassmann harmonic analysis can be performed and what are the Q-representations of such a generalized Heisenberg group. As in the conventional case, the Schrödinger and Bargmann-Fock realizations are shown to exist. The Grassmann-Hermite polynomials via the generalized Bargmann transform are presented and new Grassmann-Laguerre polynomials are obtained.
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Frydryszak, A. The fermionic Heisenberg group and its Q-representations. Lett Math Phys 26, 105–114 (1992). https://doi.org/10.1007/BF00398807
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