On a class of double cosets in reductive algebraic groups
| dc.creator | Lu, Jiang-Hua | |
| dc.creator | Yakimov, Milen | |
| dc.date | 2004-10-01 | |
| dc.date | 2005-01-20 | |
| dc.date.accessioned | 2026-07-07T05:12:45Z | |
| dc.date.available | 2026-07-07T05:12:45Z | |
| dc.description | We study a class of double coset spaces R_A \backslash G_1 \times G_2 /R_C, where G_1 and G_2 are connected reductive algebraic groups, and R_A and R_C are certain spherical subgroups of G_1 \times G_2 obtained by ``identifying'' Levi factors of parabolic subgroups in G_1 and G_2. Such double cosets naturally appear in the symplectic leaf decompositions of Poisson homogeneous spaces of complex reductive groups with the Belavin-Drinfeld Poisson structures. They also appear in orbit decompositions of the De Concini-Procesi compactifications of semi-simple groups of adjoint type. We find explicit parametrizations of the double coset spaces and describe the double cosets as homogeneous spaces of R_A \times R_C. We further show that all such double cosets give rise to set-theoretical solutions to the quantum Yang-Baxter equation on unipotent algebraic groups. | |
| dc.description | AMS-Latex, 24 pages | |
| dc.identifier | https://arxiv.org/abs/math/0410006 | |
| dc.identifier | http://arxiv.org/abs/math/0410006 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72699 | |
| dc.subject | Representation Theory | |
| dc.subject | Combinatorics | |
| dc.title | On a class of double cosets in reductive algebraic groups | |
| dc.type | text |