The Harish-Chandra isomorphism for Clifford algebras
| dc.creator | Bazlov, Yuri | |
| dc.date | 2008-12-11 | |
| dc.date | 2009-04-22 | |
| dc.date.accessioned | 2026-07-07T13:06:39Z | |
| dc.date.available | 2026-07-07T13:06:39Z | |
| dc.description | We study the analogue of the Harish-Chandra homomorphism where the universal enveloping algebra is replaced by the Clifford algebra, $Cl(g)$, of a semisimple Lie algebra $g$. Two main goals are achieved. First, we prove that there is a Harish-Chandra type isomorphism between the subalgebra of $g$-invariants in $Cl(g)$ and the Clifford algebra of the Cartan subalgebra of $g$. Second, the Cartan subalgebra is identified, via this isomorphism, with a graded space of the so-called primitive skew-symmetric invariants of $g$. This leads to a distinguished orthogonal basis of the Cartan subalgebra, which turns out to be induced from the Lie algebra Langlands dual to $g$ via the action of its principal three-dimensional subalgebra. This settles a conjecture of Kostant. | |
| dc.description | v2: added references | |
| dc.identifier | https://arxiv.org/abs/0812.2059 | |
| dc.identifier | http://arxiv.org/abs/0812.2059 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/227846 | |
| dc.subject | Representation Theory | |
| dc.title | The Harish-Chandra isomorphism for Clifford algebras | |
| dc.type | text |