Given a root system, the Weyl chambers in the co-weight lattice give rise to a real toric variety, called the real toric variety associated with the Weyl chambers. We compute the integral cohomology groups of real toric varieties associated with the Weyl chambers of type Cn and Dn, completing the computation for all classical types.
The authors are grateful to Professor Boram Park for her invaluable comments on the initial version of this paper. The authors also thank the anonymous reviewer for his/her careful reading and helpful comments on the original manuscript. The first author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (NRF-2016R1D1A1A09917654). The second author was partially supported by KAKENHI, Grant-in-Aid for Scientific Research (C) 18K03304.
