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 Tr. Mat. Inst. Steklova, 2000, Volume 228, Pages 155–167 (Mi tm498)

Conformal Theories, BRST Formalism and Representations of the Lie Superalgebras

A. V. Voronin, S. S. Horuzhy

Abstract: The results in the theory of representations of the Lie superalgebras are discussed which were obtained in the framework of a variant of the quantum BRST formalism developed by the authors. The central object of the study in this variant is the complete algebra $\mathcal A$ of the BRST symmetry which coincides with the Lie superalgebra $l(1,1)$. The set of these results presents a nearly complete description of the theory of representations of $\mathcal A$. For infinite-dimensional representations, the criteria characterizing physical representations are established and a class of representations of $\mathcal A$ by unbounded operators in Krein spaces is constructed which is sufficiently large for all physical applications; all the problems concerning the operator domains are rigorously taken into account. For finite-dimensional representations, the complete solution of the decomposition problem is presented. All the series of irreducible and indecomposable representations of $\mathcal A$ are explicitly described and all cases which do not admit any decomposition over these series are singled out and reduced to definite unsolvable algebraic problems.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2000, 228, 145–157

Bibliographic databases:
UDC: 517.9

Citation: A. V. Voronin, S. S. Horuzhy, “Conformal Theories, BRST Formalism and Representations of the Lie Superalgebras”, Problems of the modern mathematical physics, Collection of papers dedicated to the 90th anniversary of academician Nikolai Nikolaevich Bogolyubov, Tr. Mat. Inst. Steklova, 228, Nauka, MAIK «Nauka/Inteperiodika», M., 2000, 155–167; Proc. Steklov Inst. Math., 228 (2000), 145–157

Citation in format AMSBIB
\Bibitem{VorHor00} \by A.~V.~Voronin, S.~S.~Horuzhy \paper Conformal Theories,~BRST Formalism and Representations of the Lie Superalgebras \inbook Problems of the modern mathematical physics \bookinfo Collection of papers dedicated to the 90th anniversary of academician Nikolai Nikolaevich Bogolyubov \serial Tr. Mat. Inst. Steklova \yr 2000 \vol 228 \pages 155--167 \publ Nauka, MAIK «Nauka/Inteperiodika» \publaddr M. \mathnet{http://mi.mathnet.ru/tm498} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1782579} \zmath{https://zbmath.org/?q=an:0986.81106} \transl \jour Proc. Steklov Inst. Math. \yr 2000 \vol 228 \pages 145--157