Intersection of harmonics and Capelli identities for symmetric pairs

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概要

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• We consider a see-saw pair consisting of a Hermitian symmetric pair (GR, KR) and a compact symmetric pair (MR, HR), where (GR, HR) and (KR, MR) form a real reductive dual pair in a large symplectic group. In this setting, we get Capelli identities which explicitly represent certain KC-invariant elements in U(\mathfrak{g}C) in terms of HC-invariant elements in U(\mathfrak{m}C). The corresponding HC-invariant elements are called Capelli elements. We also give a decomposition of the intersection of O2n-harmonics and Sp2n-harmonics as a module of GLn = O2n ∩ Sp2n, and construct a basis for the GLn highest weight vectors. This intersection is in the kernel of our Capelli elements.

• 社団法人 日本数学会の論文
• 2008-10-01

著者

• Lee Soo

  Department Of Chemistry (bk21) And Research Institute Of Natural Science Gyeongsang National Univers

• NISHIYAMA Kyo

  Department of Mathematical Sciences, Faculty of Integrated Human Studies,Kyoto University

• Lee Soo

  Department Of Mathematics National University Of Singapore

• WACHI Akihito

  Division of Comprehensive Education Hokkaido Institute of Technology

• Nishiyama Kyo

  Department Of Mathematics Graduate School Of Science Kyoto University

• Lee Soo

  Department Of Agricultural Chemistry The University Of Tokyo

• Nishiyama Kyo

  Department Of Mathematical Sciences Faculty Of Integrated Human Studies Kyoto University

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