Parafermionic algebras, their modules and cohomologies
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-Poincar\'e 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.
Cite
@article{arxiv.1402.7091,
title = {Parafermionic algebras, their modules and cohomologies},
author = {Todor Popov},
journal= {arXiv preprint arXiv:1402.7091},
year = {2014}
}
Comments
10 pages, talk presented at the International Workshop "Lie theory and its applications in Physics" (17-23 June 2013, Varna, Bulgaria)