SOME REMARKABLE DEGENERATIONS OF QUANTUM GROUPS

Authors
DECONCINI C KAC VG PROCESI C
Citation
C. Deconcini et al., SOME REMARKABLE DEGENERATIONS OF QUANTUM GROUPS, Communications in Mathematical Physics, 157(2), 1993, pp. 405-427
Citations number
14
Categorie Soggetti
Mathematical Method, Physical Science","Physycs, Mathematical
Journal title
Communications in Mathematical Physics → ACNP
ISSN journal
00103616
Volume
157
Issue
2
Year of publication
1993
Pages
405 - 427
Database
ISI
SICI code
0010-3616(1993)157:2<405:SRDOQG>2.0.ZU;2-D
Abstract
We show that an irreducible representation of a quantized enveloping a lgebra U(epsilon) at a l(th) root of 1 has maximal dimension (= l(N)) if the corresponding symplectic leaf has maximal dimension (= 2N). The method of the proof consists of a construction of a sequence of degen erations of U(epsilon), the last one being a q-commutative algebra U(e psilon)(2N). This allows us to reduce many problems concerning U(epsil on) to that concerning U(epsilon)(2N).