Paths and Kostka--Macdonald Polynomials

Details Paths and Kostka--Macdonald Polynomials Paths and Kostka--Macdonald Polynomials

2008-11-07

arxiv.org/abs/0811.1085v2

Moscow Mathematical Journal 9 (2009) 823--854

Mathematics

Quantum Algebra

35 pages, minor revision, final version

Scientific paper

We give several equivalent combinatorial descriptions of the space of states for the box-ball systems, and connect certain partition functions for these models with the q-weight multiplicities of the tensor product of the fundamental representations of the Lie algebra gl(n). As an application, we give an elementary proof of the special case t=1 of the Haglund--Haiman--Loehr formula. Also, we propose a new class of combinatorial statistics that naturally generalize the so-called energy statistics.

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