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Non-symmetric Cauchy kernels for the classical groups

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Title: Non-symmetric Cauchy kernels for the classical groups
Authors: Fu, Amy M.1 fu@nankai.edu.cn, Lascoux, Alain2 alain.lascoux@univ-mlv.fr
Source: Journal of Combinatorial Theory - Series A. May2009, Vol. 116 Issue 4, p903-917. 15p.
Subjects: Nonsymmetric matrices, Cauchy problem, Kernel functions, Group theory, Polynomials, Mathematical analysis
Abstract: Abstract: We give non-symmetric versions of the Cauchy kernel and Littlewood''s kernels, corresponding to the types A, B, C and D, of the classical groups. Defining two families of key polynomials (one of them being the Demazure characters), we show that these new kernels are diagonal in the basis of key polynomials. We define scalar products such that the two families of key polynomials are adjoint to each other. [Copyright &y& Elsevier]
Copyright of Journal of Combinatorial Theory - Series A is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 37352281
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: Non-symmetric Cauchy kernels for the classical groups
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  Data: <searchLink fieldCode="AR" term="%22Fu%2C+Amy+M%2E%22">Fu, Amy M.</searchLink><relatesTo>1</relatesTo><i> fu@nankai.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Lascoux%2C+Alain%22">Lascoux, Alain</searchLink><relatesTo>2</relatesTo><i> alain.lascoux@univ-mlv.fr</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Combinatorial+Theory+-+Series+A%22">Journal of Combinatorial Theory - Series A</searchLink>. May2009, Vol. 116 Issue 4, p903-917. 15p.
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  Data: <searchLink fieldCode="DE" term="%22Nonsymmetric+matrices%22">Nonsymmetric matrices</searchLink><br /><searchLink fieldCode="DE" term="%22Cauchy+problem%22">Cauchy problem</searchLink><br /><searchLink fieldCode="DE" term="%22Kernel+functions%22">Kernel functions</searchLink><br /><searchLink fieldCode="DE" term="%22Group+theory%22">Group theory</searchLink><br /><searchLink fieldCode="DE" term="%22Polynomials%22">Polynomials</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+analysis%22">Mathematical analysis</searchLink>
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  Data: Abstract: We give non-symmetric versions of the Cauchy kernel and Littlewood''s kernels, corresponding to the types A, B, C and D, of the classical groups. Defining two families of key polynomials (one of them being the Demazure characters), we show that these new kernels are diagonal in the basis of key polynomials. We define scalar products such that the two families of key polynomials are adjoint to each other. [Copyright &y& Elsevier]
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  Data: <i>Copyright of Journal of Combinatorial Theory - Series A is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1016/j.jcta.2008.10.007
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 15
        StartPage: 903
    Subjects:
      – SubjectFull: Nonsymmetric matrices
        Type: general
      – SubjectFull: Cauchy problem
        Type: general
      – SubjectFull: Kernel functions
        Type: general
      – SubjectFull: Group theory
        Type: general
      – SubjectFull: Polynomials
        Type: general
      – SubjectFull: Mathematical analysis
        Type: general
    Titles:
      – TitleFull: Non-symmetric Cauchy kernels for the classical groups
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            NameFull: Fu, Amy M.
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            NameFull: Lascoux, Alain
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              M: 05
              Text: May2009
              Type: published
              Y: 2009
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              Value: 116
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              Value: 4
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            – TitleFull: Journal of Combinatorial Theory - Series A
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