منابع مشابه
Commutative Families of the Elliptic Macdonald Operator
In the paper [J. Math. Phys. 50 (2009), 095215, 42 pages], Feigin, Hashizume, Hoshino, Shiraishi, and Yanagida constructed two families of commuting operators which contain the Macdonald operator (commutative families of the Macdonald operator). They used the Ding–Iohara–Miki algebra and the trigonometric Feigin–Odesskii algebra. In the previous paper [arXiv:1301.4912], the present author const...
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This is a joint work with Evgeny Sklyanin. Using the Lax operator formalism, we construct a family of pairwise commuting operators such that the Macdonald symmetric functions of infinitely many variables and of two parameters q,t are their eigenfunctions. We express our operators in terms of the Hall-Littlewood symmetric functions of the same variables and of the parameter t corresponding to th...
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The two parameter family of coefficients Kλμ(q, t) introduced by Macdonald are conjectured to (q, t) count the standard tableaux of shape λ. If this conjecture is correct, then there exist statistics aμ(T ) and bμ(T ) such that the family of symmetric functions Hμ[X; q, t] = ∑ λKλμ(q, t)sλ[X] are generating functions for the standard tableaux of size |μ| in the sense that Hμ[X; q, t] = ∑ T q aμ...
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We give an interpretation of the t = 1 specialization of the modified Macdonald polynomial as a generating function of the energy statistics defined on the set of paths arising in the context of Box-Ball Systems (BBS-paths for short). We also introduce one parameter generalizations of the energy statistics on the set of BBS-paths which all, conjecturally, have the same distribution. Résumé. Nou...
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ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2010
ISSN: 1687-0247,1073-7928
DOI: 10.1093/imrn/rnq233