The restricted Kirillov-Reshetikhin modules for the current and twisted current algebras

Abstract

We define a family of graded restricted modules for the polynomial current algebra associated to a simple Lie algebra. We study the graded character of these modules and show that they are the same as the graded characters of certain Demazure modules. In particular, we see that the specialized characters are the same as those of the Kirillov Reshetikhin modules for quantum affine algebras.

23 pages. Minor corrections. Version to appear in Comm. Math. Phys

References in corpus (5)

• Construction of perfect crystals conjecturally corresponding to Kirillov-Reshetikhin modules over twisted quantum affine algebras
• Finite-Dimensional Crystals B^{2,s} for Quantum Affine Algebras of type D_{n}^{(1)}
• Weyl, Fusion and Demazure modules for the current algebra of sl_{r+1}
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• Local Weyl modules and cyclicity of tensor products for Yangians
• Twisted Demazure modules, fusion product decomposition and twisted Q--systems
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• Quivers with relations arising from Koszul algebras of $\mathfrak{g}$-invariants
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• Fusion Product Structure of Demazure Modules
• Quantum Q-systems and fermionic sums -- the non-simply laced case
• A categorical approach to Weyl modules
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• Weyl modules, Demazure modules, KR-modules, crystals, fusion products and limit constructions
• Character formulae and a realization of tilting modules for ${\mathfrak{sl}}_2[t]$
• Non-Minimality of Certain Irregular Coherent Preminimal Affinizations
• Graded limits of simple tensor product of Kirillov-Reshetikhin modules for $U_q({\widetilde{\mathfrak{sl}}}_{n+1})$
• Tilting Modules in Truncated Categories
• Tensor products of Kirillov-Reshetikhin modules and fusion products
• On Truncated Weyl Modules
• Restricted limits of minimal affinizations
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• Tensor products and intertwining operators between two uniserial representations of the Galilean Lie algebra $\mathfrak{sl}(2)⋉{\mathfrak{h}}_n$
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