Journal of Lie Theory

no. 1
A Note on the Fusion Product Decomposition of Demazure Modules
Journal of Lie Theory, Volume 32 (2022) no. 1, pp. 261-266
We settle the fusion product decomposition theorem for higher level affine Demazure modules for the cases $E^{(1)}_{6, 7, 8}, F^{(1)}_4$ and $E^{(2)}_{6},$ thus completing the main theorems of V.\,Chari et al. [J. Algebra 455 (2016) 314--346] and D.\,Kus et al. [Representation Theory 20 (2016) 94--127]. We obtain a new combinatorial proof for the key fact, that was used in Chari et al. (op. cit.), to prove this decomposition theorem. We give a case free uniform proof for this key fact.
DOI: 10.5802/jolt.1229
Classification: 17B10, 17B22, 17B65
Keywords: Current algebras, Demazure modules, Steinberg decomposition, affine Weyl groups 
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     title = {A {Note} on the {Fusion} {Product} {Decomposition} of {Demazure} {Modules}},
     journal = {Journal of Lie Theory},
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     year = {2022},
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R. Venkatesh; S. Viswanath. A Note on the Fusion Product Decomposition of Demazure Modules. Journal of Lie Theory, Volume 32 (2022) no. 1, pp. 261-266. doi: 10.5802/jolt.1229

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