Vector-Valued Jack Polynomials from Scratch
نویسندگان
چکیده
منابع مشابه
Vector-Valued Jack Polynomials from Scratch
Vector-valued Jack polynomials associated to the symmetric group SN are polynomials with multiplicities in an irreducible module of SN and which are simultaneous eigenfunctions of the Cherednik–Dunkl operators with some additional properties concerning the leading monomial. These polynomials were introduced by Griffeth in the general setting of the complex reflections groups G(r, p,N) and studi...
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Polynomials with values in an irreducible module of the symmetric group can be given the structure of a module for the rational Cherednik algebra, called a standard module. This algebra has one free parameter and is generated by differential-difference (“Dunkl”) operators, multiplication by coordinate functions and the group algebra. By specializing Griffeth’s (arχiv:0707.0251) results for the ...
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For each irreducible module of the symmetric group on N objects there is a set of parametrized nonsymmetric Jack polynomials in N variables taking values in the module. These polynomials are simultaneous eigenfunctions of a commutative set of operators, self-adjoint with respect to certain Hermitian forms. These polynomials were studied by the author and J.-G. Luque using a Yang–Baxter graph te...
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For each irreducible module of the symmetric group SN there is a set of parametrized nonsymmetric Jack polynomials in N variables taking values in the module. These polynomials are simultaneous eigenfunctions of a commutative set of operators, self-adjoint with respect to two Hermitian forms, one called the contravariant form and the other is with respect to a matrix-valued measure on the N -to...
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ژورنال
عنوان ژورنال: Symmetry, Integrability and Geometry: Methods and Applications
سال: 2011
ISSN: 1815-0659
DOI: 10.3842/sigma.2011.026