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
rvenkat@iisc.ac.in
Sankaran Viswanath
Institute of Mathematical Sciences, Homi Bhabha National Institute, Chennai, India
svis@imsc.res.in
[Abstract-pdf]
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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