In 1994, Lusztig developed the theory of total positivity for
arbitrary split real reductive groups and their flag manifolds. Later
the theory has found important applications in different areas: cluster
algebras, higher Teichmuller theory, the theory of amplituhedron in
physics, etc.
Recently, Lusztig initiated the study of Kac-Moody monoids over
arbitrary semifield and their flag manifolds. In the case where the
Kac-Moody datum comes from a real reductive group and the semifield is
$\mathbb R_{>0}$, the Kac-Moody monoid over $\mathbb R_{>0}$ is exactly
the totally nonnegative part of the real reductive group.
In this talk, I will discuss my joint work with Huanchen Bao on the flag
manifolds $\mathcal B(K)$ over arbitrary semifield $K$ and associated to
any Kac-Moody? datum $G$. We show that $\mathcal B(K)$ admits a natural
action of the Kac-Moody monoid $G(K)$ and admits a decomposition into
cells.

NOTE: This is a zoom seminar, and

zoom URL: https://kyoto-u-edu.zoom.us/j/87521586296
passcode: The minimal dimension of the smallest non-trivial irreducible representation of the Monster group over $\mathbb C$