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arXiv · 1402.7091

Parafermionic algebras, their modules and cohomologies

Todor Popov
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Abstract

We explore the Fock spaces of the parafermionic algebra introduced by H.S. Green. Each parafermionic Fock space allows for a free minimal resolution by graded modules of the graded 2-step nilpotent subalgebra of the parafermionic creation operators. Such a free resolution is constructed with the help of a classical Kostant's theorem computing Lie algebra cohomologies of the nilpotent subalgebra with values in the parafermionic Fock space. The Euler-Poincaré characteristics of the parafermionic Fock space free resolution yields some interesting identities between Schur polynomials. Finally we briefly comment on parabosonic and general parastatistics Fock spaces.

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Todor Popov. 2014-02-27. Parafermionic algebras, their modules and cohomologies. https://arxiv.org/abs/1402.7091

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