- LLT polynomial
In mathematics, an LLT polynomial is one of a family of symmetric functions introduced by Alain Lascoux, Bernard Leclerc, and Jean-Yves Thibon (1997) as "q"-analogues of products of
Schur function s.J. Haglund, M. Haiman, N. Loehr (2005) showed how to expand
Macdonald polynomial s in therms of LLT polynomials.Ian Grojnowski andMark Haiman (preprint) proved a positivity conjecture for LLT polynomials that combined with the previous result implies theMacdonald positivity conjecture forMacdonald polynomials , and extended the definition of LLT polynomials to arbitrary finite root systems.References
*I. Grojnowski, M. Haiman, "Affine algebras and positivity" (preprint available [http://math.berkeley.edu/~mhaiman/ here] )
*J. Haglund, M. Haiman, N. Loehr [http://arxiv.org/abs/math/0409538 A Combinatorial Formula for Macdonald Polynomials] MathSciNet|id=2138143 J. Amer. Math. Soc. 18 (2005), no. 3, 735--761
*Alain Lascoux, Bernard Leclerc, and Jean-Yves Thibon [http://arXiv.org/q-alg/9512031 Ribbon Tableaux, Hall-Littlewood Functions, Quantum Affine Algebras and Unipotent Varieties] MathSciNet|id=1434225 J. Math. Phys. 38 (1997), no. 2, 1041-1068.
Wikimedia Foundation. 2010.
