The Graded Heisenberg Group and its Q-Representations (The Odd Part)

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The odd sector of the Graded Heisenberg Group and its Q-representations are briefly analysed. Such a structure is connected to the quantization of odd mechanical systems possessing the Buttin bracket (antibracket) description in the phase space. Schrödinger Q-representation of this graded group is obtained over the graded commutative algebra of ‘doubly’ complex numbers having two imaginary units with different parity. Grassmannian special functions related to this picture are introduced.

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