Scholarlink

<p>We examine the Jack character matrix. Formulas for its determinant are derived, the roots of the determinant as a&#xa0;polynomial in terms of&#xa0;<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation> are found, and a&#xa0;combinatorial interpretation of their multiplicities is given. The second column of this matrix is calculated. We also examine the matrices of transitions between the monomial basis, the power sum basis, and the Jack polynomial basis, into whose product the Jack character matrix is decomposed. We establish recursive formulas for calculating some elements of these matrices.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

ALGEBRAIC AND COMBINATORIAL PROPERTIES OF JACK CHARACTERS

  • 期刊论文

  • 发表日期：

    2026年3月25日

查看全文
  • A. K. Voronin,
  • A. L. Kanunnikov

摘要

We examine the Jack character matrix. Formulas for its determinant are derived, the roots of the determinant as a polynomial in terms of  \(\alpha \) α are found, and a combinatorial interpretation of their multiplicities is given. The second column of this matrix is calculated. We also examine the matrices of transitions between the monomial basis, the power sum basis, and the Jack polynomial basis, into whose product the Jack character matrix is decomposed. We establish recursive formulas for calculating some elements of these matrices.