| Title |
Quasitriangular coideal subalgebras of Uq(g) in terms of generalized Satake diagrams / |
| Authors |
Regelskis, Vidas ; Vlaar, Bart |
| DOI |
10.1112/blms.12360 |
| Full Text |
|
| Is Part of |
Bulletin of the London Mathematical Society.. Hoboken : Wiley. 2020, vol. 52, no. 4, p. 693-715.. ISSN 0024-6093. eISSN 1469-2120 |
| Keywords [eng] |
coideal subalgebras ; quantum symmetric pairs ; Satake diagrams |
| Abstract [eng] |
Let g be a finite-dimensional semisimple complex Lie algebra and θ an involutive automorphism of g. According to G. Letzter, S. Kolb and M. Balagović the fixed-point subalgebra k=gθ has a quantum counterpart B, a coideal subalgebra of the Drinfeld-Jimbo quantum group Uq(g) possessing a universal K-matrix K. The objects θ, k, B and K can all be described in terms of Satake diagrams. In the present work we extend this construction to generalized Satake diagrams, combinatorial data first considered by A. Heck. A generalized Satake diagram naturally defines a semisimple automorphism θ of g restricting to the standard Cartan subalgebra h as an involution. It also defines a subalgebra k⊂g satisfying k∩h=hθ, but not necessarily a fixed-point subalgebra. The subalgebra k can be quantized to a coideal subalgebra of Uq(g) endowed with a universal K-matrix in the sense of Kolb and Balagović. We conjecture that all such coideal subalgebras of Uq(g) arise from generalized Satake diagrams in this way. |
| Published |
Hoboken : Wiley |
| Type |
Journal article |
| Language |
English |
| Publication date |
2020 |
| CC license |
|
