Geometric realizations of affine Kac-Moody algebras

Vyacheslav Futorny , Libor K\v{r}i\v{z}ka , Petr Somberg

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classification 🧮 math.RT math-phmath.AGmath.FAmath.MPmath.OA

keywords affinealgebrasgeometrickac-moodyrealizationsassociatedcasescertain

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The goal of the present paper is to obtain new free field realizations of affine Kac-Moody algebras motivated by geometric representation theory for generalized flag manifolds of finite-dimensional semisimple Lie groups. We provide an explicit construction of a large class of irreducible modules associated with certain parabolic subalgebras covering all known special cases.

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Geometric realizations of affine Kac-Moody algebras

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