Is there any character formula for demazure modules in arbitary kac moody settings which does not use demazure operators?



character formula for demazure modules
Ryom-Hansen, Steen(DK-CPNH)
Littelmann's refined Demazure character formula revisited. (English summary) 
Sém. Lothar. Combin. 49 (2002/04), Art. B49d, 10 pp.


The review:


"The author provides a purely combinatorial proof the Demazure character formula, a generalisation of Weyl's character formula. This is done using only the combinatorial properties of crystals, namely Kashiwara's crystal operators and the ∗-operation. Prior proofs required an appeal to either representation theory or Littelmann's path models."


