Classification of spherical nilpotent orbits for $U(p,p)$

Nishiyama, Kyo

Nishiyama, Kyo

J. Math. Kyoto Univ., Tome 44 (2004) no. 4, p. 203-215 / Harvested from Project Euclid

Résumé

We consider the symmetric pair $(G,K) = (U(p, q), U(p) \times U(q))$. For this pair, we classify spherical nilpotent $K_{\mathbb{C}}$-orbits which are theta lift in the stable range. For the pair $(G,K) = (U(p, p), U(p) \times U(p))$ where $p = q$, we prove that a spherical nilpotent $K_{\mathbb{C}}$-orbit must be a theta lift. As a consequence, we get a complete classification of the spherical nilpotent $K_{\mathbb{C}}$-orbits for the symmetric pair $(U(p, p), U(p) \times U(p))$.

Publié le : 2004-05-15
Classification: 22E46

@article{1250283590,
     author = {Nishiyama, Kyo},
     title = {Classification of spherical nilpotent orbits for $U(p,p)$},
     journal = {J. Math. Kyoto Univ.},
     volume = {44},
     number = {4},
     year = {2004},
     pages = { 203-215},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1250283590}
}

Nishiyama, Kyo. Classification of spherical nilpotent orbits for $U(p,p)$. J. Math. Kyoto Univ., Tome 44 (2004) no. 4, pp.  203-215. http://gdmltest.u-ga.fr/item/1250283590/