2-Component BKP Grassmannian and Simple Singularities of Type D.

It was proved in 2010 that the principal Kac–Wakimoto hierarchy of type |$D$| is a reduction of the 2-component BKP hierarchy. On the other hand, it is known that the total descendant potential of a singularity of type |$D$| is a tau-function of the principal Kac–Wakimoto hierarchy. We find explicitly the point in the Grassmannian of the 2-component BKP hierarchy (in the sense of Shiota) that corresponds to the total descendant potential. We also prove that the space of tau-functions of Gaussian type is parametrized by the base of the miniversal unfolding of the simple singularity of type |$D$|⁠. [ABSTRACT FROM AUTHOR]