Lie superalgebras and irreducibility of A_1^(1)-modules at the critical level

Details Lie superalgebras and irreducibility of A_1^(1)-modules at the critical level Lie superalgebras and irreducibility of A_1^(1)-modules at the critical level

2006-02-09

arxiv.org/abs/math/0602181v1

Communications in Mathematical Physics 270 (2007) 141-161

Mathematics

Quantum Algebra

21 pages, Latex

Scientific paper

We introduce the infinite-dimensional Lie superalgebra ${\mathcal A}$ and construct a family of mappings from certain category of ${\mathcal A}$-modules to the category of A_1^(1)-modules of critical level. Using this approach, we prove the irreducibility of a family of A_1^(1)-modules at the critical level. As a consequence, we present a new proof of irreducibility of certain Wakimoto modules. We also give a natural realizations of irreducible quotients of relaxed Verma modules and calculate characters of these representations.

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