Is there any character formula for demazure modules in arbitary kac moody settings which does not use demazure operators?
RyomHansen, Steen(DKCPNH) 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." 


Littelmann's, which gives a positive formula (counting Littelmann paths). His ICM address is here: http://www.mathunion.org/ICM/ICM1994.1/Main/icm1994.1.0298.0308.ocr.pdf He proves its validity using Demazure operators  I hope that doesn't disqualify it! 

