Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 60, Number 4 (2008), 955-982.
Intersection of harmonics and Capelli identities for symmetric pairs
We consider a see-saw pair consisting of a Hermitian symmetric pair and a compact symmetric pair , where and form a real reductive dual pair in a large symplectic group. In this setting, we get Capelli identities which explicitly represent certain -invariant elements in in terms of -invariant elements in . The corresponding -invariant elements are called Capelli elements.
We also give a decomposition of the intersection of -harmonics and -harmonics as a module of , and construct a basis for the highest weight vectors. This intersection is in the kernel of our Capelli elements.
J. Math. Soc. Japan, Volume 60, Number 4 (2008), 955-982.
First available in Project Euclid: 5 November 2008
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 17B35: Universal enveloping (super)algebras [See also 16S30]
Secondary: 22E46: Semisimple Lie groups and their representations 16S32: Rings of differential operators [See also 13N10, 32C38] 15A15: Determinants, permanents, other special matrix functions [See also 19B10, 19B14]
LEE, Soo Teck; NISHIYAMA, Kyo; WACHI, Akihito. Intersection of harmonics and Capelli identities for symmetric pairs. J. Math. Soc. Japan 60 (2008), no. 4, 955--982. doi:10.2969/jmsj/06040955. https://projecteuclid.org/euclid.jmsj/1225894029