Irreducible representations of simple Lie algebras by differential operatorsстатья
Статья опубликована в высокорейтинговом журнале
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Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 22 декабря 2021 г.
Авторы:
Morozov A.,
Reva M.,
Tselousov N.,
Zenkevich Y.
Аннотация:We describe a systematic method to construct arbitrary highest-weight modules, including arbitrary finite-dimensional representations, for any finite dimensional simple Lie algebra g. The Lie algebra generators are represented as first order differential operators in 12(dimg−rankg) variables. All rising generators e are universal in the sense that they do not depend on representation, the weights enter (in a very simple way) only in the expressions for the lowering operators f. We present explicit formulas of this kind for the simple root generators of all classical Lie algebras.