The bar involution for quantum symmetric pairs

We construct a bar involution for quantum symmetric pair coideal subalgebras $B_{\mathbf{c},\mathbf{s}}$ corresponding to involutive automorphisms of the second kind of symmetrizable Kac-Moody algebras. To this end we give unified presentations of these algebras in terms of generators and relations extending previous results by G. Letzter and the second named author. We specify precisely the set of parameters $\mathbf{c}$ for which such an intrinsic bar involution exists.Comment: Minor revision: proof of Proposition 2.3 expanded; added new Remarks 2.8, 3.1, and 3.14; simplified base field in Section 3.3; typos corrected; final version; 25 page

Radiation hydrodynamics integrated in the code PLUTO

The transport of energy through radiation is very important in many astrophysical phenomena. In dynamical problems the time-dependent equations of radiation hydrodynamics have to be solved. We present a newly developed radiation-hydrodynamics module specifically designed for the versatile MHD code PLUTO. The solver is based on the flux-limited diffusion approximation in the two-temperature approach. All equations are solved in the co-moving frame in the frequency independent (grey) approximation. The hydrodynamics is solved by the different Godunov schemes implemented in PLUTO, and for the radiation transport we use a fully implicit scheme. The resulting system of linear equations is solved either using the successive over-relaxation (SOR) method (for testing purposes), or matrix solvers that are available in the PETSc library. We state in detail the methodology and describe several test cases in order to verify the correctness of our implementation. The solver works in standard coordinate systems, such as Cartesian, cylindrical and spherical, and also for non-equidistant grids. We have presented a new radiation-hydrodynamics solver coupled to the MHD-code \PLUTO that is a modern, versatile and efficient new module for treating complex radiation hydrodynamical problems in astrophysics. As test cases, either purely radiative situations, or full radiation-hydrodynamical setups (including radiative shocks and convection in accretion discs) have been studied successfully. The new module scales very well on parallel computers using MPI. For problems in star or planet formation, we have added the possibility of irradiation by a central source.Comment: 13 pages, 11 figures, accepted by Astronomy & Astrophysic

Braid group actions on coideal subalgebras of quantized enveloping algebras

We construct braid group actions on coideal subalgebras of quantized enveloping algebras which appear in the theory of quantum symmetric pairs. In particular, we construct an action of the semidirect product of Z^n and the classical braid group in n strands on the coideal subalgebra corresponding to the symmetric pair (sl_{2n}(C), sp_{2n}(C)). This proves a conjecture by Molev and Ragoucy. We expect similar actions to exist for all symmetric Lie algebras. The given actions are inspired by Lusztig's braid group action on quantized enveloping algebras and are defined explicitly on generators. Braid group and algebra relations are verified with the help of the package Quagroup within the computer algebra program GAP.Comment: 22 page