Abstract
Abstract
3D (3 dimensional) Young diagrams are a generalization of 2D Young diagrams. In this paper, We consider 3D Bosons and 3-Jack polynomials. We associate three parameters h1, h2, h3 to y, x, z-axis respectively. 3-Jack polynomials are polynomials of Pn,j, n ≥ j with coefficients in ℂ(h1, h2, h3), which are the generalization of Schur functions and Jack polynomials to 3D case. Similar to Schur functions, 3-Jack polynomials can also be determined by the vertex operators and the Pieri formulas.
Publisher
Springer Science and Business Media LLC
Subject
Nuclear and High Energy Physics
Reference22 articles.
1. W. Fulton and J. Harris, Representation theory, a first course, Springer, New York, NY, U.S.A. (2004).
2. I.G. Macdonald, Symmetric functions and Hall polynomials, Clarendon Press, Oxford, U.K. (1979).
3. H. Weyl, The classical groups; their invariants and representations, Princeton University Press, Princeton, NJ, U.S.A. (1946).
4. T. Miwa, E. Date and M. Jimbo, Solitons: differential equations, symmetries and infinite dimensional algebras, Cambridge University Press, Cambridge, U.K. (2000) [INSPIRE].
5. N. Tsilevich, Quantum inverse scattering method for the q-boson model and symmetric functions, Funct. Anal. Appl. 40 (2006) 207 [math-ph/0510073].
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