The harmonic transvector algebra in two vector variables

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• 作者：Hendrik De Bie^a ; ^{Hendrik.DeBie@UGent.be} ; David Eelbode^b ; ^{david.eelbode@uantwerpen.be} ; Matthias Roels^b ; ^{matthias.roels@uantwerpen.be}
• 关键词：42B35 ; 17B10 ; 30G35
• 刊名：Journal of Algebra
• 出版年：2017
• 出版时间：1 March 2017
• 年：2017
• 卷：473
• 期：Complete
• 页码：247-282
• 全文大小：551 K
• 卷排序：473

文摘

The decomposition of polynomials of one vector variable into irreducible modules for the orthogonal group is a crucial result in harmonic analysis which makes use of the Howe duality theorem and leads to the study of spherical harmonics. The aim of the present paper is to describe a decomposition of polynomials in two vector variables and to obtain projection operators on each of the irreducible components. To do so, a particular transvector algebra will be used as a new dual partner for the orthogonal group leading to a generalisation of the classical Howe duality. The results are subsequently used to obtain explicit projection operators and formulas for integration of polynomials over the associated Stiefel manifold.