DUAL PAIRS, SPHERICAL-HARMONICS AND A CAPELLI IDENTITY IN QUANTUM GROUP

Authors
NOUMI M UMEDA T WAKAYAMA M
Citation
M. Noumi et al., DUAL PAIRS, SPHERICAL-HARMONICS AND A CAPELLI IDENTITY IN QUANTUM GROUP, Compositio mathematica, 104(3), 1996, pp. 227-277
Citations number
27
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Compositio mathematica → ACNP
ISSN journal
0010437X
Volume
104
Issue
3
Year of publication
1996
Pages
227 - 277
Database
ISI
SICI code
0010-437X(1996)104:3<227:DPSAAC>2.0.ZU;2-I
Abstract
A quantum analogue of the dual pair (sl(2), O-n) is constructed and it s detailed investigation is worked out. The main results include a qua ntum version of the theory of spherical harmonics, the Capelli identit y, and the first fundamental theorem of invariant theory. Also a descr iption of Casimir elements of the twisted q-deformed algebra U-q(O-n) is given in relation to the Reflection Equations.