Correlation functions of the Schur process through Macdonald difference operators
نویسنده
چکیده
Introduced by Okounkov and Reshetikhin in 2003, the Schur Process has been shown to be a determinantal point process, so that each of its correlation functions are determinants of minors of one correlation kernel matrix. In previous papers, this was derived using determinantal expressions of the skew-Schur functions; in this paper, we obtain this result in a different way, using the fact that the skew-Schur functions are eigenfunctions of the Macdonald difference operators.
منابع مشابه
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We show that the action of classical operators associated to the Mac-donald polynomials on the basis of Schur functions, S λ [X(t − 1)/(q − 1)], can be reduced to addition in λ−rings. This provides explicit formulas for the Macdonald polynomials expanded in this basis as well as in the ordinary Schur basis, S λ [X], and the monomial basis, m λ [X].
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Symmetric functions are vital to the study of combinatorics because they provide valuable information about partitions and permutations, topics which constitute the core of the subject. The significance of symmetric function theory is manifest by its connections to other branches of mathematics, including group theory, representation theory, Lie algebras, and algebraic geometry. One important b...
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عنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 131 شماره
صفحات -
تاریخ انتشار 2015