Intersection of harmonics and Capelli identities for symmetric pairs

• Lee Soo Teck

  Department of Mathematics, National University of Singapore

• Nishiyama Kyo

  Department of Mathematics, Graduate School of Science, Kyoto University

• Wachi Akihito

  Division of Comprehensive Education, Hokkaido Institute of Technology

抄録

We consider a see-saw pair consisting of a Hermitian symmetric pair (G_R, K_R) and a compact symmetric pair (M_R, H_R), where (G_R, H_R) and (K_R, M_R) form a real reductive dual pair in a large symplectic group. In this setting, we get Capelli identities which explicitly represent certain K_C-invariant elements in U(\mathfrak{g}_C) in terms of H_C-invariant elements in U(\mathfrak{m}_C). The corresponding H_C-invariant elements are called Capelli elements. <br>We also give a decomposition of the intersection of O_2n-harmonics and Sp_2n-harmonics as a module of GL_n = O_2n ∩ Sp_2n, and construct a basis for the GL_n highest weight vectors. This intersection is in the kernel of our Capelli elements.

収録刊行物

• Ｊｏｕｒｎａｌ　ｏｆ　ｔｈｅ　Ｍａｔｈｅｍａｔｉｃａｌ　Ｓｏｃｉｅｔｙ　ｏｆ　Ｊａｐａｎ

  Ｊｏｕｒｎａｌ　ｏｆ　ｔｈｅ　Ｍａｔｈｅｍａｔｉｃａｌ　Ｓｏｃｉｅｔｙ　ｏｆ　Ｊａｐａｎ 60 (4), 955-982, 2008

  一般社団法人 日本数学会

キーワード

• harmonics
• Capelli identity
• Weil representation
• invariant theory

詳細情報

• CRID: 1390001205114687488
• NII論文ID: 10024905179
• NII書誌ID: AA0070177X
• DOI: 10.2969/jmsj/06040955
• ISSN: 18811167
• ISSN: 18812333
• ISSN: 00255645
• NDL書誌ID: 9691617
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I9691617
• 本文言語コード: en
• データソース種別:
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