Atomic decomposition of characters and crystals

Lascoux stated that the type A Kostka-Foulkes polynomials K?,?(t) expand positively in terms of so-called atomic polynomials. For any semisimple Lie algebra, former polynomial is a t-analogue multiplicity dominant weight ? irreducible representation highest ?. We formulate decomposition arbitrary type, and view it as strengthening monotonicity K?,?(t). also define combinatorial version decomposition, modified crystal graph. prove this stronger holds (which provides new, conceptual approach to Lascoux's statement), types B, C, D stable range for t=1, well some other cases, while we conjecture more generally. Another stemming from our work leads an efficient computation give geometric interpretation.