Irreducible Integrable Highest Weight Research Articles

Classification of irreducible integrable highest weight modules for current Kac–Moody algebras

This paper classifies irreducible, integrable highest weight modules for “current Kac–Moody Algebras” with finite-dimensional weight spaces. We prove that these modules turn out to be modules of appropriate direct sums of finitely many copies of Kac–Moody Lie algebras.

Skew Schur Functions and Yangian Actions on Irreducible Integrable Modules of $ \hat{\frak g \frak l} _N $

An action of the Yangian of the general linear Lie algebra \( {\frak g \frak l} _N \) is defined on every irreducible integrable highest weight module of \( \hat{\frak g \frak l} _N \). This action is derived, by means of the Drinfeld duality and a subsequent semi-infinite limit, from a certain induced representation of the degenerate double affine Hecke algebra \( \frak H \). Each vacuum module of \( \hat{\frak g \frak l} _N \) is decomposed into irreducible Yangian representations by means of the intertwiners of \( \frak H \). Components of this decomposition are parameterized by semi-infinite skew Young diagrams. The decomposition gives rise to a character formulas for the modules of \( \hat{\frak g \frak l} _N \) in terms of skew Schur functions.

Level Two Standard D(2)I+1-Modules

In this paper we study the level two standard (i.e., irreducible integrable highest weight) modules for an affine Lie algebra D(2)l+1 (l ≥ 2). In particular, we give explicit constructions of these modules in the principal picture.

Level two standard [formula omitted]-modules

In this paper we study the level two standard (i.e., irreducible integrable highest weight) modules for an affine special linear Lie algebra of arbitrary rank. In particular, we give explicit realizations of these modules in the principal picture.

Realization of the level one standard 𝐶̃_{2𝑘+1}-modules

In this paper we study the level one standard (or irreducible integrable highest weight) modules for the affine symplectic Lie algebras. In particular, we give concrete realizations of all level one standard modules for the affine symplectic Lie algebras of even rank.