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Stability of the Chari-Pressley-Loktev bases for local Weyl modules of \(\mathfrak{sl}_2[t]\). (English) Zbl 1353.17012

Summary: We prove stability of the Chari-Pressley-Loktev bases for natural inclusions of local Weyl modules of the current algebra \(\mathfrak {sl}_2[t]\). These modules being known to be Demazure submodules in the level 1 representations of the affine Lie algebra \(\widehat {\mathfrak {sl}_2}\), we obtain, by passage to the direct limit, bases for the level 1 representations themselves.

MSC:

17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
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