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Journal of Lie Theory 32 (2022), No. 1, 261--266
Copyright Heldermann Verlag 2022

A Note on the Fusion Product Decomposition of Demazure Modules

Rajendran Venkatesh
Dept. of Mathematics, Indian Institute of Science, Bangalore, India

Sankaran Viswanath
Institute of Mathematical Sciences, Homi Bhabha National Institute, Chennai, India


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.

Keywords: Current algebras, Demazure modules, Steinberg decomposition, affine Weyl groups.

MSC: 17B10, 17B22, 17B65.

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