RIMS - 1654 Paths and Kostka - Macdonald Polynomials
نویسنده
چکیده
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. Mathematics Subject Classification (2000) 05E10, 20C35.
منابع مشابه
Composition Kostka functions
Macdonald defined two-parameter Kostka functions Kλμ(q, t) where λ, μ are partitions. The main purpose of this paper is to extend his definition to include all compositions as indices. Following Macdonald, we conjecture that also these more general Kostka functions are polynomials in q and t with non-negative integers as coefficients. If q = 0 then our Kostka functions are Kazhdan-Lusztig polyn...
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