Abstract:
We investigate the Jack character matrix. Formulas for its determinant are derived, its roots as a polynomial in terms of $\alpha$ are found, a combinatorial interpretation of their multiplicities is given. The second column of this matrix is computed. We also investigate matrices of transitions between the monomial, power, and Jack polynomial bases, into which the Jack character matrix is decomposed, in particular; we establish recursive formulas for computing some elements of these matrices.
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